Added MPO compression for Finite and Infinite MPO Hamiltonians#458
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Added MPO compression for Finite and Infinite MPO Hamiltonians#458TymoteuszTula wants to merge 1 commit into
TymoteuszTula wants to merge 1 commit into
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Your PR requires formatting changes to meet the project's style guidelines. Click here to view the suggested changes.diff --git a/src/operators/mpocompression.jl b/src/operators/mpocompression.jl
index 9691abf..3ddc644 100644
--- a/src/operators/mpocompression.jl
+++ b/src/operators/mpocompression.jl
@@ -24,7 +24,7 @@ as described in: https://arxiv.org/pdf/1909.06341.
function mpo_compression end
-function mpo_compression(H::FiniteMPOHamiltonian, η::Number=10^-8)
+function mpo_compression(H::FiniteMPOHamiltonian, η::Number = 10^-8)
t = @elapsed begin
# make sure that the MPO have at least three sites
N = length(H)
@@ -32,7 +32,8 @@ function mpo_compression(H::FiniteMPOHamiltonian, η::Number=10^-8)
# change MPO from N x 1 x 1 x M blocks to 3 x 1 x 1 x 3 block structure
TT = TensorMap{scalartype(H), spacetype(H[1]), 2, 2, Vector{scalartype(H)}}
Hnew = Vector{SparseBlockTensorMap{TT, scalartype(H), spacetype(H[1]), 2, 2, 4}}(
- undef, N)
+ undef, N
+ )
for n in 1:N
Hnew[n] = SparseBlockTensorMap(reduce_blocks_mpo(H[n]))
end
@@ -41,21 +42,21 @@ function mpo_compression(H::FiniteMPOHamiltonian, η::Number=10^-8)
TT = AbstractTensorMap{scalartype(H), spacetype(H), 2, 2}
Cs = Vector{SparseBlockTensorMap{TT, scalartype(H), spacetype(H), 2, 2, 4}}(undef, N)
Cs[1] = Qs[1]
- Rs = Vector{AbstractBlockTensorMap}(undef, N-2)
+ Rs = Vector{AbstractBlockTensorMap}(undef, N - 2)
R = id(codomain(Qs[2])[1])
- for n in 2:N-1
- @tensor Qnew[a,i;j,b] := R[a,c] * Qs[n][c,i;j,b]
+ for n in 2:(N - 1)
+ @tensor Qnew[a, i; j, b] := R[a, c] * Qs[n][c, i; j, b]
Q, R = qr_block_respecting(Qnew)
# For now it is safe to assume that R will be 3x3 blocked BlockTensorMap,
# since it went through right_canonical_mpo_finite first
M, R′ = decompose_R(R)
U, S, V′ = block_respecting_svd(M, η)
- @tensor C[a,i;j,b] := Q[a,i;j,c] * U[c,b]
- @tensor R[a;b] := S[a,c] * V′[c,d] * R′[d,b]
+ @tensor C[a, i; j, b] := Q[a, i; j, c] * U[c, b]
+ @tensor R[a;b] := S[a, c] * V′[c, d] * R′[d, b]
Cs[n] = C
- Rs[n-1] = R
+ Rs[n - 1] = R
end
- @tensor Cnew[a,i;j,b] := R[a,c] * Qs[N][c,i;j,b]
+ @tensor Cnew[a, i; j, b] := R[a, c] * Qs[N][c, i; j, b]
Cs[N] = Cnew
# Last step: Make new Cs into FiniteMPOHamiltonian
# TA = AbstractTensorMap{scalartype(H), spacetype(H), 2, 2}
@@ -66,10 +67,10 @@ function mpo_compression(H::FiniteMPOHamiltonian, η::Number=10^-8)
Hᵪ = Vector{Hᵪtype}(undef, N)
for n in 1:N
W = SparseBlockTensorMap(Cs[n])
- A = W[2:(end-1), 1, 1, 2:(end-1)]
- B = removeunit(W[2:(end-1), 1, 1, end], 4)
- C = removeunit(W[1,1,1,2:(end-1)], 1)
- D = removeunit(removeunit(W[1,1,1,end:end], 4), 1)
+ A = W[2:(end - 1), 1, 1, 2:(end - 1)]
+ B = removeunit(W[2:(end - 1), 1, 1, end], 4)
+ C = removeunit(W[1, 1, 1, 2:(end - 1)], 1)
+ D = removeunit(removeunit(W[1, 1, 1, end:end], 4), 1)
W = JordanMPOTensor(space(W), A, B, C, D)
Hᵪ[n] = W
end
@@ -78,27 +79,28 @@ function mpo_compression(H::FiniteMPOHamiltonian, η::Number=10^-8)
# Print reduction data
tot_dim_original = total_virt_dimension(H)
tot_dim_compressed = total_virt_dimension(Hᵪ)
- printstyled("┌───────────────────────────────────────\n", color=:cyan)
- printstyled("| MPO Compression performed succesfully\n", color=:cyan)
- printstyled("│ ⏱ Time: ", color=:cyan)
- printstyled("$(round(t, digits=1)) s\n", color=:yellow)
- printstyled("| Initial total virtual dimensions: ", color=:cyan)
- printstyled("$(tot_dim_original)\n", color=:yellow)
- printstyled("| Final total virtual dimensions: ", color=:cyan)
- printstyled("$(tot_dim_compressed)\n", color=:yellow)
+ printstyled("┌───────────────────────────────────────\n", color = :cyan)
+ printstyled("| MPO Compression performed succesfully\n", color = :cyan)
+ printstyled("│ ⏱ Time: ", color = :cyan)
+ printstyled("$(round(t, digits = 1)) s\n", color = :yellow)
+ printstyled("| Initial total virtual dimensions: ", color = :cyan)
+ printstyled("$(tot_dim_original)\n", color = :yellow)
+ printstyled("| Final total virtual dimensions: ", color = :cyan)
+ printstyled("$(tot_dim_compressed)\n", color = :yellow)
printstyled("└───────────────────────────────────────\n")
return Hᵪ, Rs
end
-function mpo_compression(H::InfiniteMPOHamiltonian, η::Number=10^-8)
+function mpo_compression(H::InfiniteMPOHamiltonian, η::Number = 10^-8)
tot_dim_original = total_virt_dimension(H)
t = @elapsed begin
N = length(H) # Number of sites
# change MPO from N x 1 x 1 x M blocks to 3 x 1 x 1 x 3 block structure
TT = TensorMap{scalartype(H), spacetype(H[1]), 2, 2, Vector{scalartype(H)}}
Hnew = Vector{SparseBlockTensorMap{TT, scalartype(H), spacetype(H[1]), 2, 2, 4}}(
- undef, N)
+ undef, N
+ )
for n in 1:N
Hnew[n] = SparseBlockTensorMap(reduce_blocks_mpo(H[n]))
end
@@ -109,16 +111,16 @@ function mpo_compression(H::InfiniteMPOHamiltonian, η::Number=10^-8)
Us = Vector{BlockTensorMap}(undef, N)
Ss = Vector{BlockTensorMap}(undef, N)
Vs = Vector{BlockTensorMap}(undef, N)
- for n = 1:N
+ for n in 1:N
Us[n], Ss[n], Vs[n] = block_respecting_svd(Cs[n], η)
end
Qs = Vector{BlockTensorMap}(undef, N)
Ps = Vector{BlockTensorMap}(undef, N)
- for n = 1:N
+ for n in 1:N
# Left canonical version of compressed iMPO
- @tensor Q[a,i;j,b] := Us[mod1(n-1,N)]'[a,c] * HL[n][c,i;j,d] * Us[n][d,b]
+ @tensor Q[a, i; j, b] := Us[mod1(n - 1, N)]'[a, c] * HL[n][c, i; j, d] * Us[n][d, b]
# Right canonical version of compressed iMPO
- @tensor P[a,i;j,b] := Vs[mod1(n-1,N)][a,c] * HR[n][c,i;j,d] * Vs[n]'[d,b]
+ @tensor P[a, i; j, b] := Vs[mod1(n - 1, N)][a, c] * HR[n][c, i; j, d] * Vs[n]'[d, b]
Qs[n] = Q
Ps[n] = P
end
@@ -129,14 +131,14 @@ function mpo_compression(H::InfiniteMPOHamiltonian, η::Number=10^-8)
# Print reduction data
tot_dim_compressed = total_virt_dimension(Q̂s)
- printstyled("┌───────────────────────────────────────\n", color=:cyan)
- printstyled("| MPO Compression performed succesfully\n", color=:cyan)
- printstyled("│ ⏱ Time: ", color=:cyan)
- printstyled("$(round(t, digits=1)) s\n", color=:yellow)
- printstyled("| Initial total virtual dimensions: ", color=:cyan)
- printstyled("$(tot_dim_original)\n", color=:yellow)
- printstyled("| Final total virtual dimensions: ", color=:cyan)
- printstyled("$(tot_dim_compressed)\n", color=:yellow)
+ printstyled("┌───────────────────────────────────────\n", color = :cyan)
+ printstyled("| MPO Compression performed succesfully\n", color = :cyan)
+ printstyled("│ ⏱ Time: ", color = :cyan)
+ printstyled("$(round(t, digits = 1)) s\n", color = :yellow)
+ printstyled("| Initial total virtual dimensions: ", color = :cyan)
+ printstyled("$(tot_dim_original)\n", color = :yellow)
+ printstyled("| Final total virtual dimensions: ", color = :cyan)
+ printstyled("$(tot_dim_compressed)\n", color = :yellow)
printstyled("└───────────────────────────────────────\n")
return Q̂s, P̂s
@@ -145,13 +147,13 @@ end
# utility
# -------
function trace_single_block(d::AbstractTensorMap)
- return @tensor trd[a;b] := d[a,i;i,b]
+ return @tensor trd[a;b] := d[a, i; i, b]
end
function change_value_at_fusiontree!(T::AbstractTensorMap, i::Integer, v::Number)
# change value of the fusiontree at index i of a TensorMap T with new value v
f = fusiontrees(T)
- if f isa Vector
+ return if f isa Vector
T[f[i]...] .= v
elseif f isa Indices
T[f.values[i]...] .= v
@@ -164,7 +166,7 @@ end
function total_virt_dimension(H::FiniteMPOHamiltonian)
# calculate the sum of bond dimensions for entire H MPO
N = length(H)
- tvd = sum([dims(H[i])[4] for i in 1:N-1])
+ tvd = sum([dims(H[i])[4] for i in 1:(N - 1)])
return tvd
end
@@ -191,39 +193,49 @@ function qr_block_respecting(W::AbstractBlockTensorMap)
# traceless
id1 = id(codomain(W)[2])
- t = zeros(ComplexF64, domain(W)[2][1] ← domain(W)[2][2:end-1])
- for block in 2:blM-1
- d = W[1,1,1,block]
+ t = zeros(ComplexF64, domain(W)[2][1] ← domain(W)[2][2:(end - 1)])
+ for block in 2:(blM - 1)
+ d = W[1, 1, 1, block]
trd = trace_single_block(d)
- @tensor W[1,1,1,block][a,i;j,b] = d[a,i;j,b] - trd[a;b] * id1[i;j]
+ @tensor W[1, 1, 1, block][a, i; j, b] = d[a, i; j, b] - trd[a;b] * id1[i;j]
# Here goes the creation of matrix R' with a t' tensor
- t[block-1] = trd / dim_st[2]
+ t[block - 1] = trd / dim_st[2]
end
# Perform QR of the 2:blM-1 block
- V = W[1:blN-1, :, :, 2:blM-1]
- V = permute(V, ((1,2,3), (4,)))
-
- V = convert(SparseBlockTensorMap{TensorMap{eltype(V).parameters...},
- eltype(storagetype(V)), spacetype(V), 3, 1, 4,}, V)
+ V = W[1:(blN - 1), :, :, 2:(blM - 1)]
+ V = permute(V, ((1, 2, 3), (4,)))
+
+ V = convert(
+ SparseBlockTensorMap{
+ TensorMap{eltype(V).parameters...},
+ eltype(storagetype(V)), spacetype(V), 3, 1, 4,
+ }, V
+ )
Q, R = qr_compact(V)
- Q = permute(Q, ((1,2),(3,4)))
+ Q = permute(Q, ((1, 2), (3, 4)))
# Put Q into larger Q̂
- Q̂ = zeros(scalartype(W), codomain(W) ← domain(W)[1] ⊗ (domain(W)[2][1] ⊞ domain(Q)[2] ⊞
- domain(W)[2][end]))
- Q̂[1,1,1,1] = Q̂[end,1,1,end] = W[1,1,1,1]
- Q̂[1:end-1,1,1,2:end-1] = Q
- Q̂[1:end-1,1,1,end] = W[1:end-1,1,1,end]
+ Q̂ = zeros(
+ scalartype(W), codomain(W) ← domain(W)[1] ⊗ (
+ domain(W)[2][1] ⊞ domain(Q)[2] ⊞
+ domain(W)[2][end]
+ )
+ )
+ Q̂[1, 1, 1, 1] = Q̂[end, 1, 1, end] = W[1, 1, 1, 1]
+ Q̂[1:(end - 1), 1, 1, 2:(end - 1)] = Q
+ Q̂[1:(end - 1), 1, 1, end] = W[1:(end - 1), 1, 1, end]
# Put R and t into larger R̂
- R̂ = zeros(scalartype(W), domain(W)[2][1] ⊞ codomain(R)[1] ⊞ domain(W)[2][end] ←
- domain(W)[2][1] ⊞ domain(R)[1] ⊞ domain(W)[2][end])
- R̂[2:end-1,2:end-1] = R
- R̂[1,2:end-1] = t
- change_value_at_fusiontree!(R̂[1,1],1,1)
- change_value_at_fusiontree!(R̂[end,end],1,1)
-
+ R̂ = zeros(
+ scalartype(W), domain(W)[2][1] ⊞ codomain(R)[1] ⊞ domain(W)[2][end] ←
+ domain(W)[2][1] ⊞ domain(R)[1] ⊞ domain(W)[2][end]
+ )
+ R̂[2:(end - 1), 2:(end - 1)] = R
+ R̂[1, 2:(end - 1)] = t
+ change_value_at_fusiontree!(R̂[1, 1], 1, 1)
+ change_value_at_fusiontree!(R̂[end, end], 1, 1)
+
return Q̂, R̂
end
@@ -240,47 +252,55 @@ function lq_block_respecting(W::AbstractBlockTensorMap)
# traceless
id1 = id(codomain(W)[2])
- t = zeros(ComplexF64, codomain(W)[1][2:end-1] ← codomain(W)[1][end])
- for block in 2:blN-1
- d = W[block,1,1,end]
+ t = zeros(ComplexF64, codomain(W)[1][2:(end - 1)] ← codomain(W)[1][end])
+ for block in 2:(blN - 1)
+ d = W[block, 1, 1, end]
trd = trace_single_block(d)
- @tensor W[block,1,1,end][a,i;j,b] = d[a,i;j,b] - trd[a;b] * id1[i;j]
+ @tensor W[block, 1, 1, end][a, i; j, b] = d[a, i; j, b] - trd[a;b] * id1[i;j]
# Here goes the creation of matrix R' with a t' tensor
- t[block-1] = trd / dim_st[2]
+ t[block - 1] = trd / dim_st[2]
end
# Perform QR of the 2:blM-1 block (with virtual indices transposed)
- V = W[2:blN-1, :, :, 2:blM]
- V = permute(V, ((1,), (2,3,4)))
-
- V = convert(SparseBlockTensorMap{TensorMap{eltype(V).parameters...},
- eltype(storagetype(V)), spacetype(V), 1, 3, 4,}, V)
+ V = W[2:(blN - 1), :, :, 2:blM]
+ V = permute(V, ((1,), (2, 3, 4)))
+
+ V = convert(
+ SparseBlockTensorMap{
+ TensorMap{eltype(V).parameters...},
+ eltype(storagetype(V)), spacetype(V), 1, 3, 4,
+ }, V
+ )
# to perform QR
L, Q = lq_compact(V)
# transpose vitrual indices back (now to reconstruct initial matrix
# one has to apply R on the left)
- Q = permute(Q, ((1,2),(3,4)))
+ Q = permute(Q, ((1, 2), (3, 4)))
# Put Q into larger Q̂
- Q̂ = zeros(scalartype(W), (codomain(W)[1][1] ⊞ codomain(Q)[1] ⊞ codomain(W)[1][end]) ⊗
- codomain(W)[2] ← domain(W))
- Q̂[1,1,1,1] = Q̂[end,1,1,end] = W[1,1,1,1]
- Q̂[2:end-1,1,1,2:end] = Q
- Q̂[1,1,1,2:end] = W[1,1,1,2:end]
+ Q̂ = zeros(
+ scalartype(W), (codomain(W)[1][1] ⊞ codomain(Q)[1] ⊞ codomain(W)[1][end]) ⊗
+ codomain(W)[2] ← domain(W)
+ )
+ Q̂[1, 1, 1, 1] = Q̂[end, 1, 1, end] = W[1, 1, 1, 1]
+ Q̂[2:(end - 1), 1, 1, 2:end] = Q
+ Q̂[1, 1, 1, 2:end] = W[1, 1, 1, 2:end]
# Put L and t into larger L̂
- L̂ = zeros(scalartype(W), domain(W)[2][1] ⊞ codomain(L)[1] ⊞ domain(W)[2][end] ←
- domain(W)[2][1] ⊞ domain(L)[1] ⊞ domain(W)[2][end])
- L̂[2:end-1,2:end-1] = L
- L̂[2:end-1,end] = t
- change_value_at_fusiontree!(L̂[1,1],1,1)
- change_value_at_fusiontree!(L̂[end,end],1,1)
+ L̂ = zeros(
+ scalartype(W), domain(W)[2][1] ⊞ codomain(L)[1] ⊞ domain(W)[2][end] ←
+ domain(W)[2][1] ⊞ domain(L)[1] ⊞ domain(W)[2][end]
+ )
+ L̂[2:(end - 1), 2:(end - 1)] = L
+ L̂[2:(end - 1), end] = t
+ change_value_at_fusiontree!(L̂[1, 1], 1, 1)
+ change_value_at_fusiontree!(L̂[end, end], 1, 1)
return L̂, Q̂
end
function left_canonical_mpo_finite(
H::Union{FiniteMPOHamiltonian, V}
- ) where {T<:SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V<:Vector{T}}
+ ) where {T <: SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V <: Vector{T}}
# change finite Hamiltonian MPO into its Left canonical form. The 'H' is a
# FiniteMPOHamiltonian from MPSKit (l and r boundary conditions are already
# part of the left-most and right-most MPOs, they can not be compressed, and
@@ -295,22 +315,22 @@ function left_canonical_mpo_finite(
Qs = Vector{SparseBlockTensorMap{TT, scalartype(H), spacetype(H[1]), 2, 2, 4}}(undef, N)
Qs[1] = H[1]
Qs[2] = Q
- Rs = Vector{AbstractBlockTensorMap}(undef, N-2)
+ Rs = Vector{AbstractBlockTensorMap}(undef, N - 2)
Rs[1] = R
- for n in 3:N-1
- @tensor Wnew[a,i;j,b] := R[a,c] * H[n][c,i;j,b]
+ for n in 3:(N - 1)
+ @tensor Wnew[a, i; j, b] := R[a, c] * H[n][c, i; j, b]
Q, R = qr_block_respecting(Wnew)
Qs[n] = Q
- Rs[n-1] = R
+ Rs[n - 1] = R
end
- @tensor Wlast[a,i;j,b] := R[a,c] * H[N][c,i;j,b]
+ @tensor Wlast[a, i; j, b] := R[a, c] * H[N][c, i; j, b]
Qs[N] = Wlast
return Qs, Rs
end
function right_canonical_mpo_finite(
H::Union{FiniteMPOHamiltonian, V}
- ) where {T<:SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V<:Vector{T}}
+ ) where {T <: SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V <: Vector{T}}
# change finite Hamiltonian MPO into its Right canonical form. The 'H' is a
# FiniteMPOHamiltonian from MPSKit (l and r boundary conditions are already
# part of the left-most and right-most MPOs, they can not be compressed, and
@@ -320,20 +340,20 @@ function right_canonical_mpo_finite(
N = length(H)
@assert N ≥ 3
- L, Q = lq_block_respecting(H[end-1])
+ L, Q = lq_block_respecting(H[end - 1])
TT = AbstractTensorMap{scalartype(H), spacetype(H[1]), 2, 2}
Qs = Vector{SparseBlockTensorMap{TT, scalartype(H), spacetype(H[1]), 2, 2, 4}}(undef, N)
Qs[end] = H[end]
- Qs[end-1] = Q
- Ls = Vector{AbstractBlockTensorMap}(undef, N-2)
+ Qs[end - 1] = Q
+ Ls = Vector{AbstractBlockTensorMap}(undef, N - 2)
Ls[end] = L
- for n in N-2:-1:2
- @tensor Wnew[a,i;j,b] := H[n][a,i;j,c] * L[c,b]
+ for n in (N - 2):-1:2
+ @tensor Wnew[a, i; j, b] := H[n][a, i; j, c] * L[c, b]
L, Q = lq_block_respecting(Wnew)
Qs[n] = Q
- Ls[n-1] = L
+ Ls[n - 1] = L
end
- @tensor Wlast[a,i;j,b] := H[1][a,i;j,c] * L[c,b]
+ @tensor Wlast[a, i; j, b] := H[1][a, i; j, c] * L[c, b]
Qs[1] = Wlast
return Qs, Ls
end
@@ -341,29 +361,29 @@ end
function decompose_R(R::AbstractBlockTensorMap)
M = zeros(ComplexF64, codomain(R) ← domain(R))
R′ = zeros(ComplexF64, domain(R) ← domain(R))
- change_value_at_fusiontree!(M[1,1], 1, 1)
- change_value_at_fusiontree!(M[end,end], 1, 1)
- change_value_at_fusiontree!(R′[1,1], 1, 1)
- change_value_at_fusiontree!(R′[end,end], 1, 1)
- M[2:end-1,2:end-1] = R[2:end-1,2:end-1]
- R′[1,2:end-1] = R[1,2:end-1]
+ change_value_at_fusiontree!(M[1, 1], 1, 1)
+ change_value_at_fusiontree!(M[end, end], 1, 1)
+ change_value_at_fusiontree!(R′[1, 1], 1, 1)
+ change_value_at_fusiontree!(R′[end, end], 1, 1)
+ M[2:(end - 1), 2:(end - 1)] = R[2:(end - 1), 2:(end - 1)]
+ R′[1, 2:(end - 1)] = R[1, 2:(end - 1)]
# R′[2:end-1,2:end-1] = id(codomain(R[2,2]))
# Make diagonal matrix even with codomain and domain being different spaces
# Right now I'm assuming that each of the fusiontree is a square block
- for (s, f) in fusiontrees(R′[2:end-1,2:end-1])
+ for (s, f) in fusiontrees(R′[2:(end - 1), 2:(end - 1)])
if s.uncoupled[1] == f.uncoupled[1]
- dim = size(R′[2:end-1,2:end-1][s,f])[1]
- R′[2:end-1,2:end-1][s,f] .= diagm(ones(dim))
- end
+ dim = size(R′[2:(end - 1), 2:(end - 1)][s, f])[1]
+ R′[2:(end - 1), 2:(end - 1)][s, f] .= diagm(ones(dim))
+ end
end
return M, R′
end
-function block_respecting_svd(M::AbstractBlockTensorMap, η::Number; perform_truncation=true)
+function block_respecting_svd(M::AbstractBlockTensorMap, η::Number; perform_truncation = true)
# Perform block-respecting svd on matrix M, with precision η
- # TODO Change it so that it works when sectors are numbered by indices rather than
+ # TODO Change it so that it works when sectors are numbered by indices rather than
# enumerated
- M2 = M[2:end-1,2:end-1]
+ M2 = M[2:(end - 1), 2:(end - 1)]
U, S, V′ = svd_compact(M2)
num_sectors = length(blocksectors(S))
@@ -381,7 +401,7 @@ function block_respecting_svd(M::AbstractBlockTensorMap, η::Number; perform_tru
# end
# end
# end
-
+
# New code - works for both cases
for (n, csec) in enumerate(blocksectors(S))
new_dims[n] = blockdim(S.domain, csec)
@@ -395,7 +415,7 @@ function block_respecting_svd(M::AbstractBlockTensorMap, η::Number; perform_tru
end
fdims = Vector{Pair{sectortype(S), Int32}}()
- # Old code
+ # Old code
# for n in 1:num_sectors
# if new_dims[n] > 0
# push!(fdims, blocksectors(S)[n] => new_dims[n])
@@ -428,32 +448,34 @@ function block_respecting_svd(M::AbstractBlockTensorMap, η::Number; perform_tru
for csec in blocksectors(S_new)
cl = length(block(S_new, csec).diag)
block(S_new, csec).diag[1:end] = block(S, csec).diag[1:cl]
- block(U_new, csec)[:,:] = block(U, csec)[:,1:cl]
- block(V′_new, csec)[:,:] = block(V′, csec)[1:cl,:]
+ block(U_new, csec)[:, :] = block(U, csec)[:, 1:cl]
+ block(V′_new, csec)[:, :] = block(V′, csec)[1:cl, :]
end
Û = zeros(ComplexF64, codomain(M) ← domain(M)[1][1] ⊞ domain(U_new)[1] ⊞ domain(M)[1][end])
- Ŝ = zeros(ComplexF64, codomain(M)[1][1] ⊞ codomain(S_new)[1] ⊞ codomain(M)[1][end] ←
- domain(M)[1][1] ⊞ domain(S_new)[1] ⊞ domain(M)[1][end])
+ Ŝ = zeros(
+ ComplexF64, codomain(M)[1][1] ⊞ codomain(S_new)[1] ⊞ codomain(M)[1][end] ←
+ domain(M)[1][1] ⊞ domain(S_new)[1] ⊞ domain(M)[1][end]
+ )
V̂′ = zeros(ComplexF64, codomain(M)[1][1] ⊞ codomain(V′_new)[1] ⊞ codomain(M)[1][end] ← domain(M))
- change_value_at_fusiontree!(Û[1,1], 1, 1)
- change_value_at_fusiontree!(Û[end,end], 1, 1)
- change_value_at_fusiontree!(Ŝ[1,1], 1, 1)
- change_value_at_fusiontree!(Ŝ[end,end], 1, 1)
- change_value_at_fusiontree!(V̂′[1,1], 1, 1)
- change_value_at_fusiontree!(V̂′[end,end], 1, 1)
+ change_value_at_fusiontree!(Û[1, 1], 1, 1)
+ change_value_at_fusiontree!(Û[end, end], 1, 1)
+ change_value_at_fusiontree!(Ŝ[1, 1], 1, 1)
+ change_value_at_fusiontree!(Ŝ[end, end], 1, 1)
+ change_value_at_fusiontree!(V̂′[1, 1], 1, 1)
+ change_value_at_fusiontree!(V̂′[end, end], 1, 1)
- Û[2:end-1,2:end-1] = U_new
- Ŝ[2,2] = S_new
- V̂′[2:end-1,2:end-1] = V′_new
+ Û[2:(end - 1), 2:(end - 1)] = U_new
+ Ŝ[2, 2] = S_new
+ V̂′[2:(end - 1), 2:(end - 1)] = V′_new
return Û, Ŝ, V̂′
end
function reduce_blocks_mpo(W::AbstractBlockTensorMap)
- # Function that copies BlockTensorMap W from N x 1 x 1 x M blocked matrix to a
- # 3 x 1 x 1 x 3 blocked matrix, with the middle block being joined dimensions of N-2,
+ # Function that copies BlockTensorMap W from N x 1 x 1 x M blocked matrix to a
+ # 3 x 1 x 1 x 3 blocked matrix, with the middle block being joined dimensions of N-2,
# M-2 blocks from the original matrix
# TODO Make exception if either N or M is smaller than 3
@@ -461,9 +483,9 @@ function reduce_blocks_mpo(W::AbstractBlockTensorMap)
if size(W)[1] ≤ 3 && size(W)[4] ≤ 3
return W
end
-
- old_cod = codomain(W)[1][2:end-1]
- old_dom = domain(W)[2][2:end-1]
+
+ old_cod = codomain(W)[1][2:(end - 1)]
+ old_dom = domain(W)[2][2:(end - 1)]
new_cod = spacetype(W)([sec => blockdim(old_cod, sec) for sec in sectors(old_cod)]...)
new_dom = spacetype(W)([sec => blockdim(old_dom, sec) for sec in sectors(old_dom)]...)
@@ -482,51 +504,51 @@ function reduce_blocks_mpo(W::AbstractBlockTensorMap)
W2 = zeros(scalartype(W), Vcod ← Vdom)
# Corners can be copied trivially
- W2[1,1,1,1] = W[1,1,1,1]
- W2[end,1,1,end] = W[end,1,1,end]
- W2[1,1,1,end] = W[1,1,1,end]
- W2[end,1,1,1] = W[end,1,1,1]
+ W2[1, 1, 1, 1] = W[1, 1, 1, 1]
+ W2[end, 1, 1, end] = W[end, 1, 1, end]
+ W2[1, 1, 1, end] = W[1, 1, 1, end]
+ W2[end, 1, 1, 1] = W[end, 1, 1, 1]
# Treat the cases with smaller codomain or domain separately
if size(W)[1] ≤ 2
# Middle upperblock
- for (s,f) in fusiontrees(W[1,1,1,2:end-1])
- W2[1,1,1,2][s,f] = W[1,1,1,2:end-1][s,f]
+ for (s, f) in fusiontrees(W[1, 1, 1, 2:(end - 1)])
+ W2[1, 1, 1, 2][s, f] = W[1, 1, 1, 2:(end - 1)][s, f]
end
- # Middle bottomblock (if size(W)[1] is 1, this is the same block as in
+ # Middle bottomblock (if size(W)[1] is 1, this is the same block as in
# previous loop)
- for (s,f) in fusiontrees(W[end,1,1,2:end-1])
- W2[end,1,1,2][s,f] = W[end,1,1,2:end-1][s,f]
+ for (s, f) in fusiontrees(W[end, 1, 1, 2:(end - 1)])
+ W2[end, 1, 1, 2][s, f] = W[end, 1, 1, 2:(end - 1)][s, f]
end
elseif size(W)[4] ≤ 2
# Middle leftblock
- for (s,f) in fusiontrees(W[2:end-1,1,1,1])
- W2[2,1,1,1][s,f] = W[2:end-1,1,1,1][s,f]
+ for (s, f) in fusiontrees(W[2:(end - 1), 1, 1, 1])
+ W2[2, 1, 1, 1][s, f] = W[2:(end - 1), 1, 1, 1][s, f]
end
# Middle rightblock (if size(W)[4] is 1, this is the same block as in previous loop)
- for (s,f) in fusiontrees(W[2:end-1,1,1,end])
- W2[2,1,1,end][s,f] = W[2:end-1,1,1,end][s,f]
+ for (s, f) in fusiontrees(W[2:(end - 1), 1, 1, end])
+ W2[2, 1, 1, end][s, f] = W[2:(end - 1), 1, 1, end][s, f]
end
else
# All other blocks can be dealt with fusiontrees
# Middle block (most important)
- for (s,f) in fusiontrees(W[2:end-1,1,1,2:end-1])
- W2[2,1,1,2][s,f] = W[2:end-1,1,1,2:end-1][s,f]
+ for (s, f) in fusiontrees(W[2:(end - 1), 1, 1, 2:(end - 1)])
+ W2[2, 1, 1, 2][s, f] = W[2:(end - 1), 1, 1, 2:(end - 1)][s, f]
end
# Upper block
- for (s,f) in fusiontrees(W[1,1,1,2:end-1])
- W2[1,1,1,2][s,f] = W[1,1,1,2:end-1][s,f]
+ for (s, f) in fusiontrees(W[1, 1, 1, 2:(end - 1)])
+ W2[1, 1, 1, 2][s, f] = W[1, 1, 1, 2:(end - 1)][s, f]
end
# Bottom block
- for (s,f) in fusiontrees(W[end,1,1,2:end-1])
- W2[3,1,1,2][s,f] = W[end,1,1,2:end-1][s,f]
+ for (s, f) in fusiontrees(W[end, 1, 1, 2:(end - 1)])
+ W2[3, 1, 1, 2][s, f] = W[end, 1, 1, 2:(end - 1)][s, f]
end
# Left block
- for (s,f) in fusiontrees(W[2:end-1,1,1,1])
- W2[2,1,1,1][s,f] = W[2:end-1,1,1,1][s,f]
+ for (s, f) in fusiontrees(W[2:(end - 1), 1, 1, 1])
+ W2[2, 1, 1, 1][s, f] = W[2:(end - 1), 1, 1, 1][s, f]
end
# Right block
- for (s,f) in fusiontrees(W[2:end-1,1,1,end])
- W2[2,1,1,3][s,f] = W[2:end-1,1,1,end][s,f]
+ for (s, f) in fusiontrees(W[2:(end - 1), 1, 1, end])
+ W2[2, 1, 1, 3][s, f] = W[2:(end - 1), 1, 1, end][s, f]
end
end
return W2
@@ -536,10 +558,10 @@ function check_how_far_from_id(R::AbstractBlockTensorMap)
# Function checking how far the diagonal elements of R are from either
# +1 or -1. Assume R is 3x3 and [1,1] and [3,3] blocks are always id
tdev = 0
- for (s,f) in fusiontrees(R[2,2])
+ for (s, f) in fusiontrees(R[2, 2])
if s.uncoupled[1] == f.uncoupled[1]
- for d in size(R[2,2][s,f])[1]
- tdev += min(abs(R[2,2][s,f][d,d] - 1), abs(R[2,2][s,f][d,d] + 1))
+ for d in size(R[2, 2][s, f])[1]
+ tdev += min(abs(R[2, 2][s, f][d, d] - 1), abs(R[2, 2][s, f][d, d] + 1))
end
end
end
@@ -547,7 +569,7 @@ function check_how_far_from_id(R::AbstractBlockTensorMap)
end
function create_impoham_from_mpos_msites(Qs::Vector{BlockTensorMap})
- # Given the Vector{BlockTensorMap} Qs, return the multisite InfiniteMPOHamiltonian
+ # Given the Vector{BlockTensorMap} Qs, return the multisite InfiniteMPOHamiltonian
N = length(Qs)
sctype = scalartype(Qs[1])
sptype = spacetype(Qs[1])
@@ -559,10 +581,10 @@ function create_impoham_from_mpos_msites(Qs::Vector{BlockTensorMap})
Cs = Vector{CType}(undef, N)
for n in 1:N
W = SparseBlockTensorMap(Qs[n])
- A = W[2:(end-1), 1, 1, 2:(end-1)]
- B = removeunit(W[2:(end-1), 1, 1, end], 4)
- C = removeunit(W[1,1,1,2:(end-1)], 1)
- D = removeunit(removeunit(W[1,1,1,end:end], 4), 1)
+ A = W[2:(end - 1), 1, 1, 2:(end - 1)]
+ B = removeunit(W[2:(end - 1), 1, 1, end], 4)
+ C = removeunit(W[1, 1, 1, 2:(end - 1)], 1)
+ D = removeunit(removeunit(W[1, 1, 1, end:end], 4), 1)
W = JordanMPOTensor(space(W), A, B, C, D)
Cs[n] = W
end
@@ -572,8 +594,8 @@ end
function left_canonical_mpo_infinite_iter_msites(
H::Union{InfiniteMPOHamiltonian, V},
- η=10^-10
- ) where {T<:SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V<:Vector{T}}
+ η = 10^-10
+ ) where {T <: SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V <: Vector{T}}
# Return the left_canonical form of the iMPO, H can have multiple sites in the unit cell
N = length(H) # Number of sites
@@ -581,8 +603,8 @@ function left_canonical_mpo_infinite_iter_msites(
Ls = fill(id(ComplexF64, codomain(H[1])[1]), N)
Rs = fill(id(ComplexF64, codomain(H[1])[1]), N)
Q = similar(H[1])
- printstyled("┌─── Started iterative left orthogonalization ────\n", color=:cyan)
- while sum(εs)/N > η
+ printstyled("┌─── Started iterative left orthogonalization ────\n", color = :cyan)
+ while sum(εs) / N > η
# First store the R matrices and change them H into Qs
for n in 1:N
Q, R = qr_block_respecting(H[n])
@@ -593,28 +615,28 @@ function left_canonical_mpo_infinite_iter_msites(
end
# Then assign R[(n+1)//N] * Q[n] to H[n]
for n in 1:N
- @tensor H[n][a,i;j,b] = Rs[mod1(n-1,N)][a;c] * H[n][c,i;j,b]
+ @tensor H[n][a, i; j, b] = Rs[mod1(n - 1, N)][a;c] * H[n][c, i; j, b]
end
- printstyled("| total err = $(sum(εs)/N)\n", color=:white)
+ printstyled("| total err = $(sum(εs) / N)\n", color = :white)
end
- printstyled("└─── Left orthogonalization finished correctly ──\n", color=:cyan)
+ printstyled("└─── Left orthogonalization finished correctly ──\n", color = :cyan)
return H, Ls
end
function right_canonical_mpo_infinite_iter_msites(
H::Union{InfiniteMPOHamiltonian, V},
- η=10^-10
- ) where {T<:SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V<:Vector{T}}
- # Return the right_canonical form of the iMPO, H can have multiple sites in the unit
+ η = 10^-10
+ ) where {T <: SparseBlockTensorMap{<:Any, <:Any, <:Any, 2, 2, 4}, V <: Vector{T}}
+ # Return the right_canonical form of the iMPO, H can have multiple sites in the unit
# cell
N = length(H) # Number of sites
-
+
εs = fill(Inf, N)
Rs = fill(id(ComplexF64, codomain(H[1])[1]), N)
Ls = fill(id(ComplexF64, codomain(H[1])[1]), N)
Q = similar(H[N])
- printstyled("┌─── Started iterative right orthogonalization ────\n", color=:cyan)
- while sum(εs)/N > η
+ printstyled("┌─── Started iterative right orthogonalization ────\n", color = :cyan)
+ while sum(εs) / N > η
# First store the R matrices and change them H into Qs
for n in N:-1:1
L, Q = lq_block_respecting(H[n])
@@ -625,10 +647,10 @@ function right_canonical_mpo_infinite_iter_msites(
end
# Then assign R[(n+1)//N] * Q[n] to H[n]
for n in N:-1:1
- @tensor H[n][a,i;j,b] = H[n][a,i;j,c] * Ls[mod1(n+1, N)][c,b]
+ @tensor H[n][a, i; j, b] = H[n][a, i; j, c] * Ls[mod1(n + 1, N)][c, b]
end
- printstyled("| total err = $(sum(εs)/N)\n", color=:white)
+ printstyled("| total err = $(sum(εs) / N)\n", color = :white)
end
- printstyled("└─── Right orthogonalization finished correctly ──\n", color=:cyan)
+ printstyled("└─── Right orthogonalization finished correctly ──\n", color = :cyan)
return Rs, H
-end
\ No newline at end of file
+end
diff --git a/test/operators/finite_mpo_compression.jl b/test/operators/finite_mpo_compression.jl
index 07c259c..8b4cf3d 100644
--- a/test/operators/finite_mpo_compression.jl
+++ b/test/operators/finite_mpo_compression.jl
@@ -17,24 +17,28 @@ end
# Utility functions to create Hamiltonians for testing
function create_long_range_ising_symmetries_finite(M, k)
- chain = fill(Z2Space(0=>1, 1=>1), M)
+ chain = fill(Z2Space(0 => 1, 1 => 1), M)
ZZ = S_zz(Z2Irrep)
X = S_x(Z2Irrep)
single_site_operators = [i => X for i in 1:M]
- two_site_operators = [(i,i+j) => ZZ for i in 1:M for j in 1:k if i+j ≤ M]
- H = FiniteMPOHamiltonian(chain, single_site_operators...,
- two_site_operators...)
+ two_site_operators = [(i, i + j) => ZZ for i in 1:M for j in 1:k if i + j ≤ M]
+ H = FiniteMPOHamiltonian(
+ chain, single_site_operators...,
+ two_site_operators...
+ )
return H
end
function create_long_range_ising_symmetries_random_finite(M, k, σⱼ, σₕ)
- chain = fill(Z2Space(0=>1, 1=>1), M)
+ chain = fill(Z2Space(0 => 1, 1 => 1), M)
ZZ = S_zz(Z2Irrep)
X = S_x(Z2Irrep)
single_site_operators = [i => (σₕ * randn()) * X for i in 1:M]
- two_site_operators = [(i,i+j) => (1 + σⱼ * randn()) * ZZ for i in 1:M for j in 1:k if i+j ≤ M]
- H = FiniteMPOHamiltonian(chain, single_site_operators...,
- two_site_operators...)
+ two_site_operators = [(i, i + j) => (1 + σⱼ * randn()) * ZZ for i in 1:M for j in 1:k if i + j ≤ M]
+ H = FiniteMPOHamiltonian(
+ chain, single_site_operators...,
+ two_site_operators...
+ )
return H
end
@@ -108,15 +112,15 @@ end
range = 4 # cutoff for the maximum range between interactions
trunc_st = notrunc()
- mps = FiniteMPS(L, Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
+ mps = FiniteMPS(L, Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
H = create_long_range_ising_symmetries_finite(L, range)
- find_groundstate!(mps, H, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps, H, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0 = expectation_value(mps, H)
#println("<mps|H|mps> = $real(E0)")
- mps2 = FiniteMPS(L, Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
+ mps2 = FiniteMPS(L, Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
H2, Rs = mpo_compression(H)
- find_groundstate!(mps2, H2, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2, H2, DMRG2(; maxiter = 100, trscheme = trunc_st))
E1 = expectation_value(mps2, H2)
end
@@ -126,50 +130,50 @@ end
trunc_st = trunctol()
mps1 = FiniteMPS(M, ℂ^2, ℂ^D)
- mps2 = FiniteMPS(M, Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
- mps3 = FiniteMPS(M, Vect[FermionParity](0=>1, 1=>1), Vect[FermionParity](0=>D, 1=>D))
+ mps2 = FiniteMPS(M, Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
+ mps3 = FiniteMPS(M, Vect[FermionParity](0 => 1, 1 => 1), Vect[FermionParity](0 => D, 1 => D))
H1 = transverse_field_ising_trivial_finite(M)
H2 = transverse_field_ising_z2_finite(M)
H3 = transverse_field_ising_fermion_parity_finite(M)
# Find groundstate of non-compressed Hamiltonian
- find_groundstate!(mps1, H1, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1, H1, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1 = expectation_value(mps1, H1)
- find_groundstate!(mps2, H2, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2, H2, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2 = expectation_value(mps2, H2)
- find_groundstate!(mps3, H3, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps3, H3, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_3 = expectation_value(mps3, H3)
# Compress MPO
mps1c = FiniteMPS(M, ℂ^2, ℂ^D)
- mps2c = FiniteMPS(M, Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
- mps3c = FiniteMPS(M, Vect[FermionParity](0=>1, 1=>1), Vect[FermionParity](0=>D, 1=>D))
+ mps2c = FiniteMPS(M, Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
+ mps3c = FiniteMPS(M, Vect[FermionParity](0 => 1, 1 => 1), Vect[FermionParity](0 => D, 1 => D))
H1c, _ = mpo_compression(H1, 10^-10)
H2c, _ = mpo_compression(H2, 10^-10)
H3c, _ = mpo_compression(H3, 10^-10)
# Find groundstate of compressed Hamiltonian
- find_groundstate!(mps1c, H1c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1c, H1c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1c = expectation_value(mps1c, H1c)
- find_groundstate!(mps2c, H2c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2c, H2c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2c = expectation_value(mps2c, H2c)
- find_groundstate!(mps3c, H3c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps3c, H3c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_3c = expectation_value(mps3c, H3c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
@assert E0_2 ≈ E0_2c
@assert E0_3 ≈ E0_3c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
println("Max dim uncompressed H2: $(max_dim_ham(H2)) || Max dim compressed H2c:
- $(max_dim_ham(H2c))" )
+ $(max_dim_ham(H2c))")
println("Max dim uncompressed H3: $(max_dim_ham(H3)) || Max dim compressed H3c:
- $(max_dim_ham(H3c))" )
+ $(max_dim_ham(H3c))")
end
@@ -178,29 +182,29 @@ end
D = 10 # Max bond dimension
trunc_st = trunctol()
- mps1 = FiniteMPS(M, Vect[FermionParity](0=>1, 1=>1), Vect[FermionParity](0=>D, 1=>D))
+ mps1 = FiniteMPS(M, Vect[FermionParity](0 => 1, 1 => 1), Vect[FermionParity](0 => D, 1 => D))
H1 = kitaev_model_finite(M)
# Find groundstate of non-compressed Hamiltonian
- find_groundstate!(mps1, H1, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1, H1, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1 = expectation_value(mps1, H1)
# Compress MPO
- mps1c = FiniteMPS(M, Vect[FermionParity](0=>1, 1=>1), Vect[FermionParity](0=>D, 1=>D))
+ mps1c = FiniteMPS(M, Vect[FermionParity](0 => 1, 1 => 1), Vect[FermionParity](0 => D, 1 => D))
H1c, _ = mpo_compression(H1, 10^-10)
# Find groundstate of compressed Hamiltonian
- find_groundstate!(mps1c, H1c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1c, H1c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1c = expectation_value(mps1c, H1c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
end
@@ -210,50 +214,50 @@ end
trunc_st = trunctol()
mps1 = FiniteMPS(M, ℂ^3, ℂ^D)
- mps2 = FiniteMPS(M, U1Space(0=>1, 1=>1, -1=>1), U1Space(0=>D, 1=>D, -1=>D))
- mps3 = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1=>D))
+ mps2 = FiniteMPS(M, U1Space(0 => 1, 1 => 1, -1 => 1), U1Space(0 => D, 1 => D, -1 => D))
+ mps3 = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1 => D))
H1 = heisenberg_XXX_trivial_finite(M)
H2 = heisenberg_XXX_U1_finite(M)
H3 = heisenberg_XXX_SU2_finite(M)
# Find groundstate of non-compressed Hamiltonian
- find_groundstate!(mps1, H1, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1, H1, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1 = expectation_value(mps1, H1)
- find_groundstate!(mps2, H2, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2, H2, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2 = expectation_value(mps2, H2)
- find_groundstate!(mps3, H3, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps3, H3, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_3 = expectation_value(mps3, H3)
# Compress MPO
mps1c = FiniteMPS(M, ℂ^3, ℂ^D)
- mps2c = FiniteMPS(M, U1Space(0=>1, 1=>1, -1=>1), U1Space(0=>D, 1=>D, -1=>D))
- mps3c = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1=>D))
+ mps2c = FiniteMPS(M, U1Space(0 => 1, 1 => 1, -1 => 1), U1Space(0 => D, 1 => D, -1 => D))
+ mps3c = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1 => D))
H1c, _ = mpo_compression(H1, 10^-10)
H2c, _ = mpo_compression(H2, 10^-10)
H3c, _ = mpo_compression(H3, 10^-10)
# Find groundstate of compressed Hamiltonian
- find_groundstate!(mps1c, H1c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1c, H1c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1c = expectation_value(mps1c, H1c)
- find_groundstate!(mps2c, H2c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2c, H2c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2c = expectation_value(mps2c, H2c)
- find_groundstate!(mps3c, H3c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps3c, H3c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_3c = expectation_value(mps3c, H3c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
@assert E0_2 ≈ E0_2c
@assert E0_3 ≈ E0_3c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
println("Max dim uncompressed H2: $(max_dim_ham(H2)) || Max dim compressed H2c:
- $(max_dim_ham(H2c))" )
+ $(max_dim_ham(H2c))")
println("Max dim uncompressed H3: $(max_dim_ham(H3)) || Max dim compressed H3c:
- $(max_dim_ham(H3c))" )
+ $(max_dim_ham(H3c))")
end
@@ -263,50 +267,50 @@ end
trunc_st = trunctol()
mps1 = FiniteMPS(M, ℂ^3, ℂ^D)
- mps2 = FiniteMPS(M, U1Space(0=>1, 1=>1, -1=>1), U1Space(0=>D, 1=>D, -1=>D))
- mps3 = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1=>D))
+ mps2 = FiniteMPS(M, U1Space(0 => 1, 1 => 1, -1 => 1), U1Space(0 => D, 1 => D, -1 => D))
+ mps3 = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1 => D))
H1 = bilinear_biquadratic_model_trivial_finite(M)
H2 = bilinear_biquadratic_model_U1_finite(M)
H3 = bilinear_biquadratic_model_SU2_finite(M)
# Find groundstate of non-compressed Hamiltonian
- find_groundstate!(mps1, H1, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1, H1, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1 = expectation_value(mps1, H1)
- find_groundstate!(mps2, H2, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2, H2, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2 = expectation_value(mps2, H2)
- find_groundstate!(mps3, H3, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps3, H3, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_3 = expectation_value(mps3, H3)
# Compress MPO
mps1c = FiniteMPS(M, ℂ^3, ℂ^D)
- mps2c = FiniteMPS(M, U1Space(0=>1, 1=>1, -1=>1), U1Space(0=>D, 1=>D, -1=>D))
- mps3c = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1=>D))
+ mps2c = FiniteMPS(M, U1Space(0 => 1, 1 => 1, -1 => 1), U1Space(0 => D, 1 => D, -1 => D))
+ mps3c = FiniteMPS(M, SU2Space(1 => 1), SU2Space(1 => D))
H1c, _ = mpo_compression(H1, 10^-10)
H2c, _ = mpo_compression(H2, 10^-10)
H3c, _ = mpo_compression(H3, 10^-10)
# Find groundstate of compressed Hamiltonian
- find_groundstate!(mps1c, H1c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1c, H1c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1c = expectation_value(mps1c, H1c)
- find_groundstate!(mps2c, H2c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2c, H2c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2c = expectation_value(mps2c, H2c)
- find_groundstate!(mps3c, H3c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps3c, H3c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_3c = expectation_value(mps3c, H3c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
@assert E0_2 ≈ E0_2c
@assert E0_3 ≈ E0_3c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
println("Max dim uncompressed H2: $(max_dim_ham(H2)) || Max dim compressed H2c:
- $(max_dim_ham(H2c))" )
+ $(max_dim_ham(H2c))")
println("Max dim uncompressed H3: $(max_dim_ham(H3)) || Max dim compressed H3c:
- $(max_dim_ham(H3c))" )
+ $(max_dim_ham(H3c))")
end
@@ -316,39 +320,39 @@ end
trunc_st = trunctol()
mps1 = FiniteMPS(M, ℂ^3, ℂ^D)
- mps2 = FiniteMPS(M, Z3Space(0=>1, 1=>1, 2=>1), Z3Space(0=>1, 1=>1, 2=>1))
+ mps2 = FiniteMPS(M, Z3Space(0 => 1, 1 => 1, 2 => 1), Z3Space(0 => 1, 1 => 1, 2 => 1))
H1 = quantum_potts_trivial_finite(M)
H2 = quantum_potts_Z3_finite(M)
# Find groundstate of non-compressed Hamiltonian
- find_groundstate!(mps1, H1, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1, H1, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1 = expectation_value(mps1, H1)
- find_groundstate!(mps2, H2, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2, H2, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2 = expectation_value(mps2, H2)
# Compress MPO
mps1c = FiniteMPS(M, ℂ^3, ℂ^D)
- mps2c = FiniteMPS(M, Z3Space(0=>1, 1=>1, 2=>1), Z3Space(0=>1, 1=>1, 2=>1))
+ mps2c = FiniteMPS(M, Z3Space(0 => 1, 1 => 1, 2 => 1), Z3Space(0 => 1, 1 => 1, 2 => 1))
H1c, _ = mpo_compression(H1, 10^-10)
H2c, _ = mpo_compression(H2, 10^-10)
# Find groundstate of compressed Hamiltonian
- find_groundstate!(mps1c, H1c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps1c, H1c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_1c = expectation_value(mps1c, H1c)
- find_groundstate!(mps2c, H2c, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2c, H2c, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0_2c = expectation_value(mps2c, H2c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
@assert E0_2 ≈ E0_2c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
println("Max dim uncompressed H2: $(max_dim_ham(H2)) || Max dim compressed H2c:
- $(max_dim_ham(H2c))" )
+ $(max_dim_ham(H2c))")
end
@@ -362,14 +366,14 @@ end
range = 4 # cutoff for the maximum range between interactions
trunc_st = notrunc()
- mps = FiniteMPS(L, Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
+ mps = FiniteMPS(L, Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
H = create_long_range_ising_symmetries_random_finite(L, range, 0.3, 0.4)
- find_groundstate!(mps, H, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps, H, DMRG2(; maxiter = 100, trscheme = trunc_st))
E0 = expectation_value(mps, H)
#println("<mps|H|mps> = $real(E0)")
- mps2 = FiniteMPS(L, Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
+ mps2 = FiniteMPS(L, Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
H2, Rs = mpo_compression(H)
- find_groundstate!(mps2, H2, DMRG2(; maxiter=100, trscheme=trunc_st))
+ find_groundstate!(mps2, H2, DMRG2(; maxiter = 100, trscheme = trunc_st))
E1 = expectation_value(mps2, H2)
-end
\ No newline at end of file
+end
diff --git a/test/operators/infinite_mpo_compression.jl b/test/operators/infinite_mpo_compression.jl
index caebc96..e8fd128 100644
--- a/test/operators/infinite_mpo_compression.jl
+++ b/test/operators/infinite_mpo_compression.jl
@@ -17,37 +17,41 @@ end
# Utility functions to create Hamiltonians for testing
function create_long_range_ising_symmetries_infinite(k)
- infinite_chain = PeriodicVector([Z2Space(0=>1, 1=>1)])
+ infinite_chain = PeriodicVector([Z2Space(0 => 1, 1 => 1)])
ZZ = S_zz(Z2Irrep)
X = S_x(Z2Irrep)
- two_site_operators = [(1,j) => -ZZ for j in 1:k]
+ two_site_operators = [(1, j) => -ZZ for j in 1:k]
H = InfiniteMPOHamiltonian(infinite_chain, two_site_operators...)
return H
end
function create_long_range_ising_symmetries_infinite_msite_random(M, k, σⱼ, σₕ)
- V = Z2Space(0=>1, 1=>1)
+ V = Z2Space(0 => 1, 1 => 1)
infinite_chain = PeriodicVector(fill(V, M))
ZZ = S_zz(Z2Irrep)
X = S_x(Z2Irrep)
single_site_operators = [i => (σₕ * randn()) * X for i in 1:M]
- two_site_operators = [(i,i+j) => (1 + σⱼ * randn()) * ZZ for i in 1:M for j in 1:k]
- H = InfiniteMPOHamiltonian(infinite_chain, single_site_operators...,
- two_site_operators...)
+ two_site_operators = [(i, i + j) => (1 + σⱼ * randn()) * ZZ for i in 1:M for j in 1:k]
+ H = InfiniteMPOHamiltonian(
+ infinite_chain, single_site_operators...,
+ two_site_operators...
+ )
return H
end
function create_long_range_ising_symmetries_infinite_twosite_diff_int_strength(k, J, h)
- infinite_chain = PeriodicVector([Z2Space(0=>1, 1=>1), Z2Space(0=>1, 1=>1)])
+ infinite_chain = PeriodicVector([Z2Space(0 => 1, 1 => 1), Z2Space(0 => 1, 1 => 1)])
ZZ = S_zz(Z2Irrep)
X = S_x(Z2Irrep)
- two_site_operators_J12 = [(a,a+j) => J[1] * ZZ for a in [1 2] for j in 1:2:2k]
- two_site_operators_J11 = [(1,j) => J[2] * ZZ for j in 3:2:2k]
- two_site_operators_J22 = [(2,j) => J[3] * ZZ for j in 4:2:2k]
+ two_site_operators_J12 = [(a, a + j) => J[1] * ZZ for a in [1 2] for j in 1:2:2k]
+ two_site_operators_J11 = [(1, j) => J[2] * ZZ for j in 3:2:2k]
+ two_site_operators_J22 = [(2, j) => J[3] * ZZ for j in 4:2:2k]
single_site_operators = [1 => h[1] * X, 2 => h[2] * X]
- H = InfiniteMPOHamiltonian(infinite_chain, single_site_operators...,
- two_site_operators_J11..., two_site_operators_J12...,
- two_site_operators_J22...)
+ H = InfiniteMPOHamiltonian(
+ infinite_chain, single_site_operators...,
+ two_site_operators_J11..., two_site_operators_J12...,
+ two_site_operators_J22...
+ )
return H
end
@@ -108,9 +112,9 @@ end
range = 2 # cutoff for the maximum range between interactions
trunc_st = notrunc()
- mps = InfiniteMPS(Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
+ mps = InfiniteMPS(Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
H = create_long_range_ising_symmetries_infinite(range)
- mps, = find_groundstate(mps, H, VUMPS(;maxiter=10))
+ mps, = find_groundstate(mps, H, VUMPS(; maxiter = 10))
E0 = expectation_value(mps, H)
#println("<mps|H|mps> = $real(E0)")
@@ -118,10 +122,10 @@ end
# H2, Rs = mpo_finite_compression(H)
# find_groundstate!(mps2, H2, DMRG2(; maxiter=100, trscheme=trunc_st))
# E1 = expectation_value(mps2, H2)
- mps2 = InfiniteMPS(Z2Space(0=>1, 1=>1), Z2Space(0=>D, 1=>D))
+ mps2 = InfiniteMPS(Z2Space(0 => 1, 1 => 1), Z2Space(0 => D, 1 => D))
Q, P = mpo_compression(H)
H2 = Q
- mps2, = find_groundstate(mps2, H2, VUMPS(;maxiter=100))
+ mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter = 100))
E0 = expectation_value(mps2, H2)
end
@@ -134,12 +138,12 @@ end
J = [1, 1, 1]
h = [0.001, 0.001]
- spacephys = fill(Z2Space(0=>1, 1=>1), 2)
- space_virt = fill(Z2Space(0=>D, 1=>D), 2)
+ spacephys = fill(Z2Space(0 => 1, 1 => 1), 2)
+ space_virt = fill(Z2Space(0 => D, 1 => D), 2)
mps = InfiniteMPS(spacephys, space_virt)
H = create_long_range_ising_symmetries_infinite_twosite_diff_int_strength(range, J, h)
- mps, = find_groundstate(mps, H, VUMPS(;maxiter=100))
+ mps, = find_groundstate(mps, H, VUMPS(; maxiter = 100))
E0 = expectation_value(mps, H)
#println("<mps|H|mps> = $real(E0)")
@@ -150,7 +154,7 @@ end
mps2 = InfiniteMPS(spacephys, space_virt)
Qs, Ps = mpo_compression(H, 0)
H2 = Qs
- mps2, = find_groundstate(mps2, H2, VUMPS(;maxiter=100))
+ mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter = 100))
E0 = expectation_value(mps2, H2)
end
@@ -159,52 +163,62 @@ end
D = 10 # Max bond dimension
mps1 = InfiniteMPS(fill(ℂ^2, M), fill(ℂ^D, M))
- mps2 = InfiniteMPS(fill(Z2Space(0=>1, 1=>1), M), fill(Z2Space(0=>D, 1=>D), M))
- mps3 = InfiniteMPS(fill(Vect[FermionParity](0=>1, 1=>1), M), fill(Vect[FermionParity](
- 0=>D, 1=>D), M))
+ mps2 = InfiniteMPS(fill(Z2Space(0 => 1, 1 => 1), M), fill(Z2Space(0 => D, 1 => D), M))
+ mps3 = InfiniteMPS(
+ fill(Vect[FermionParity](0 => 1, 1 => 1), M), fill(
+ Vect[FermionParity](
+ 0 => D, 1 => D
+ ), M
+ )
+ )
H1 = transverse_field_ising_trivial_infinite(M)
H2 = transverse_field_ising_z2_infinite(M)
H3 = transverse_field_ising_fermion_parity_infinite(M)
# Find groundstate of non-compressed Hamiltonian
- mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter=100))
+ mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter = 100))
E0_1 = expectation_value(mps1, H1)
- mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter=100))
+ mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter = 100))
E0_2 = expectation_value(mps2, H2)
- mps3, = find_groundstate(mps3, H3, VUMPS(; maxiter=100))
+ mps3, = find_groundstate(mps3, H3, VUMPS(; maxiter = 100))
E0_3 = expectation_value(mps3, H3)
# Compress MPO
mps1c = InfiniteMPS(fill(ℂ^2, M), fill(ℂ^D, M))
- mps2c = InfiniteMPS(fill(Z2Space(0=>1, 1=>1), M), fill(Z2Space(0=>D, 1=>D), M))
- mps3c = InfiniteMPS(fill(Vect[FermionParity](0=>1, 1=>1), M), fill(Vect[FermionParity](
- 0=>D, 1=>D), M))
+ mps2c = InfiniteMPS(fill(Z2Space(0 => 1, 1 => 1), M), fill(Z2Space(0 => D, 1 => D), M))
+ mps3c = InfiniteMPS(
+ fill(Vect[FermionParity](0 => 1, 1 => 1), M), fill(
+ Vect[FermionParity](
+ 0 => D, 1 => D
+ ), M
+ )
+ )
H1c, _ = mpo_compression(H1, 10^-10)
H2c, _ = mpo_compression(H2, 10^-10)
H3c, _ = mpo_compression(H3, 10^-10)
# Find groundstate of compressed Hamiltonian
- mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter=100))
+ mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter = 100))
E0_1c = expectation_value(mps1c, H1c)
- mps2c, = find_groundstate(mps2c, H2c, VUMPS(; maxiter=100))
+ mps2c, = find_groundstate(mps2c, H2c, VUMPS(; maxiter = 100))
E0_2c = expectation_value(mps2c, H2c)
- mps3c, = find_groundstate(mps3c, H3c, VUMPS(; maxiter=100))
+ mps3c, = find_groundstate(mps3c, H3c, VUMPS(; maxiter = 100))
E0_3c = expectation_value(mps3c, H3c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
@assert E0_2 ≈ E0_2c
@assert E0_3 ≈ E0_3c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
println("Max dim uncompressed H2: $(max_dim_ham(H2)) || Max dim compressed H2c:
- $(max_dim_ham(H2c))" )
+ $(max_dim_ham(H2c))")
println("Max dim uncompressed H3: $(max_dim_ham(H3)) || Max dim compressed H3c:
- $(max_dim_ham(H3c))" )
+ $(max_dim_ham(H3c))")
end
@@ -212,31 +226,35 @@ end
M = 10
D = 10 # Max bond dimension
- mps1 = InfiniteMPS(fill(Vect[FermionParity](0=>1, 1=>1), M),
- fill(Vect[FermionParity](0=>D, 1=>D), M))
+ mps1 = InfiniteMPS(
+ fill(Vect[FermionParity](0 => 1, 1 => 1), M),
+ fill(Vect[FermionParity](0 => D, 1 => D), M)
+ )
H1 = kitaev_model_infinite(M)
# Find groundstate of non-compressed Hamiltonian
- mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter=100))
+ mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter = 100))
E0_1 = expectation_value(mps1, H1)
# Compress MPO
- mps1c = InfiniteMPS(fill(Vect[FermionParity](0=>1, 1=>1), M),
- fill(Vect[FermionParity](0=>D, 1=>D), M))
+ mps1c = InfiniteMPS(
+ fill(Vect[FermionParity](0 => 1, 1 => 1), M),
+ fill(Vect[FermionParity](0 => D, 1 => D), M)
+ )
H1c, _ = mpo_compression(H1, 10^-10)
# Find groundstate of compressed Hamiltonian
- mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter=100))
+ mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter = 100))
E0_1c = expectation_value(mps1c, H1c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
end
@@ -244,51 +262,51 @@ end
M = 10
D = 6 # Max bond dimension
- mps1 = InfiniteMPS(fill(ℂ^3, M),fill(ℂ^D, M))
- mps2 = InfiniteMPS(fill(U1Space(0=>1, 1=>1, -1=>1), M), fill(U1Space(0=>D, 1=>D, -1=>D), M))
- mps3 = InfiniteMPS(fill(SU2Space(1 => 1), M), fill(SU2Space(1=>D), M))
+ mps1 = InfiniteMPS(fill(ℂ^3, M), fill(ℂ^D, M))
+ mps2 = InfiniteMPS(fill(U1Space(0 => 1, 1 => 1, -1 => 1), M), fill(U1Space(0 => D, 1 => D, -1 => D), M))
+ mps3 = InfiniteMPS(fill(SU2Space(1 => 1), M), fill(SU2Space(1 => D), M))
H1 = heisenberg_XXX_trivial_infinite(M)
H2 = heisenberg_XXX_U1_infinite(M)
H3 = heisenberg_XXX_SU2_infinite(M)
# Find groundstate of non-compressed Hamiltonian
- mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter=100))
+ mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter = 100))
E0_1 = expectation_value(mps1, H1)
- mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter=100))
+ mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter = 100))
E0_2 = expectation_value(mps2, H2)
- mps3, = find_groundstate(mps3, H3, VUMPS(; maxiter=100))
+ mps3, = find_groundstate(mps3, H3, VUMPS(; maxiter = 100))
E0_3 = expectation_value(mps3, H3)
# Compress MPO
- mps1c = InfiniteMPS(fill(ℂ^3, M),fill(ℂ^D, M))
- mps2c = InfiniteMPS(fill(U1Space(0=>1, 1=>1, -1=>1), M), fill(U1Space(0=>D, 1=>D, -1=>D), M))
- mps3c = InfiniteMPS(fill(SU2Space(1 => 1), M), fill(SU2Space(1=>D), M))
+ mps1c = InfiniteMPS(fill(ℂ^3, M), fill(ℂ^D, M))
+ mps2c = InfiniteMPS(fill(U1Space(0 => 1, 1 => 1, -1 => 1), M), fill(U1Space(0 => D, 1 => D, -1 => D), M))
+ mps3c = InfiniteMPS(fill(SU2Space(1 => 1), M), fill(SU2Space(1 => D), M))
H1c, _ = mpo_compression(H1, 10^-10)
H2c, _ = mpo_compression(H2, 10^-10)
H3c, _ = mpo_compression(H3, 10^-10)
# Find groundstate of compressed Hamiltonian
- mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter=100))
+ mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter = 100))
E0_1c = expectation_value(mps1c, H1c)
- mps2c, = find_groundstate(mps2c, H2c, VUMPS(; maxiter=100))
+ mps2c, = find_groundstate(mps2c, H2c, VUMPS(; maxiter = 100))
E0_2c = expectation_value(mps2c, H2c)
- mps3c, = find_groundstate(mps3c, H3c, VUMPS(; maxiter=100))
+ mps3c, = find_groundstate(mps3c, H3c, VUMPS(; maxiter = 100))
E0_3c = expectation_value(mps3c, H3c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
@assert E0_2 ≈ E0_2c
@assert E0_3 ≈ E0_3c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
println("Max dim uncompressed H2: $(max_dim_ham(H2)) || Max dim compressed H2c:
- $(max_dim_ham(H2c))" )
+ $(max_dim_ham(H2c))")
println("Max dim uncompressed H3: $(max_dim_ham(H3)) || Max dim compressed H3c:
- $(max_dim_ham(H3c))" )
+ $(max_dim_ham(H3c))")
end
@@ -296,30 +314,30 @@ end
M = 10
D = 6 # Max bond dimension
- mps1 = InfiniteMPS(fill(ℂ^3, M),fill(ℂ^D, M))
+ mps1 = InfiniteMPS(fill(ℂ^3, M), fill(ℂ^D, M))
H1 = bilinear_biquadratic_model_trivial_infinite(M)
# Find groundstate of non-compressed Hamiltonian
- mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter=100))
+ mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter = 100))
E0_1 = expectation_value(mps1, H1)
# Compress MPO
- mps1c = InfiniteMPS(fill(ℂ^3, M),fill(ℂ^D, M))
+ mps1c = InfiniteMPS(fill(ℂ^3, M), fill(ℂ^D, M))
H1c, _ = mpo_compression(H1, 10^-10)
# Find groundstate of compressed Hamiltonian
- mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter=100))
+ mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter = 100))
E0_1c = expectation_value(mps1c, H1c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
end
@@ -328,39 +346,39 @@ end
D = 6 # Max bond dimension
mps1 = InfiniteMPS(fill(ℂ^3, M), fill(ℂ^D, M))
- mps2 = InfiniteMPS(fill(Z3Space(0=>1, 1=>1, 2=>1), M), fill(Z3Space(0=>1, 1=>1, 2=>1), M))
+ mps2 = InfiniteMPS(fill(Z3Space(0 => 1, 1 => 1, 2 => 1), M), fill(Z3Space(0 => 1, 1 => 1, 2 => 1), M))
H1 = quantum_potts_trivial_infinite(M)
H2 = quantum_potts_Z3_infinite(M)
# Find groundstate of non-compressed Hamiltonian
- mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter=100))
+ mps1, = find_groundstate(mps1, H1, VUMPS(; maxiter = 100))
E0_1 = expectation_value(mps1, H1)
- mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter=100))
+ mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter = 100))
E0_2 = expectation_value(mps2, H2)
# Compress MPO
mps1c = InfiniteMPS(fill(ℂ^3, M), fill(ℂ^D, M))
- mps2c = InfiniteMPS(fill(Z3Space(0=>1, 1=>1, 2=>1), M), fill(Z3Space(0=>1, 1=>1, 2=>1), M))
+ mps2c = InfiniteMPS(fill(Z3Space(0 => 1, 1 => 1, 2 => 1), M), fill(Z3Space(0 => 1, 1 => 1, 2 => 1), M))
H1c, _ = mpo_compression(H1, 10^-10)
H2c, _ = mpo_compression(H2, 10^-10)
# Find groundstate of compressed Hamiltonian
- mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter=100))
+ mps1c, = find_groundstate(mps1c, H1c, VUMPS(; maxiter = 100))
E0_1c = expectation_value(mps1c, H1c)
- mps2c, = find_groundstate(mps2c, H2c, VUMPS(; maxiter=100))
+ mps2c, = find_groundstate(mps2c, H2c, VUMPS(; maxiter = 100))
E0_2c = expectation_value(mps2c, H2c)
- # Assert that the ground state energies are equal up to a precision, display the
+ # Assert that the ground state energies are equal up to a precision, display the
# compression
@assert E0_1 ≈ E0_1c
@assert E0_2 ≈ E0_2c
println("Max dim uncompressed H1: $(max_dim_ham(H1)) || Max dim compressed H1c:
- $(max_dim_ham(H1c))" )
+ $(max_dim_ham(H1c))")
println("Max dim uncompressed H2: $(max_dim_ham(H2)) || Max dim compressed H2c:
- $(max_dim_ham(H2c))" )
+ $(max_dim_ham(H2c))")
end
@@ -373,16 +391,16 @@ end
L = 10 # number of sites
range = 4 # cutoff for the maximum range between interactions
- mps = InfiniteMPS(fill(Z2Space(0=>1, 1=>1),L), fill(Z2Space(0=>D, 1=>D),L))
+ mps = InfiniteMPS(fill(Z2Space(0 => 1, 1 => 1), L), fill(Z2Space(0 => D, 1 => D), L))
H = create_long_range_ising_symmetries_infinite_msite_random(L, range, 0.1, 0.001)
- mps, = find_groundstate(mps, H, VUMPS(; maxiter=100))
+ mps, = find_groundstate(mps, H, VUMPS(; maxiter = 100))
E0 = expectation_value(mps, H)
#println("<mps|H|mps> = $real(E0)")
- mps2 = InfiniteMPS(fill(Z2Space(0=>1, 1=>1),L), fill(Z2Space(0=>D, 1=>D),L))
+ mps2 = InfiniteMPS(fill(Z2Space(0 => 1, 1 => 1), L), fill(Z2Space(0 => D, 1 => D), L))
H2, Rs = mpo_compression(H, 0)
- mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter=100))
+ mps2, = find_groundstate(mps2, H2, VUMPS(; maxiter = 100))
E1 = expectation_value(mps2, H2)
@assert E0 ≈ E1
-end
\ No newline at end of file
+end |
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Added a function "mpo_compression" that is working both for FiniteMPOHamiltonian and InfiniteMPOHamiltonian. It performs a compression algorithms defined in https://arxiv.org/abs/1909.06341.