Add mixed_canonize function

src/Ansatz/Chain.jl

@@ -144,24 +144,24 @@ function rightindex(::Union{Open, Periodic}, tn::Chain, site::Site)
  end
 end
 
-canonize(tn::Chain, args...; kwargs...) = canonize!(deepcopy(tn), args...; kwargs...)
-canonize!(tn::Chain, args...; kwargs...) = canonize!(boundary(tn), tn, args...; kwargs...)
+canonize_site(tn::Chain, args...; kwargs...) = canonize_site!(deepcopy(tn), args...; kwargs...)
+canonize_site!(tn::Chain, args...; kwargs...) = canonize_site!(boundary(tn), tn, args...; kwargs...)
 
 # NOTE: in mode == :svd the spectral weights are stored in a vector connected to the now virtual hyperindex!
-function canonize!(::Open, tn::Chain, site::Site; direction::Symbol, mode = :qr)
+function canonize_site!(::Open, tn::Chain, site::Site; direction::Symbol, mode = :qr)
  left_inds = Symbol[]
  right_inds = Symbol[]
 
  virtualind = if direction === :left
- site == Site(nsites(tn)) && throw(ArgumentError("Cannot right-canonize right-most tensor"))
+ site == Site(nsites(tn)) && throw(ArgumentError("Cannot left-canonize right-most tensor"))
  push!(right_inds, rightindex(tn, site))
 
  site == Site(1) || push!(left_inds, leftindex(tn, site))
  push!(left_inds, Quantum(tn)[site])
 
  only(right_inds)
  elseif direction === :right
- site == Site(1) && throw(ArgumentError("Cannot left-canonize left-most tensor"))
+ site == Site(1) && throw(ArgumentError("Cannot right-canonize left-most tensor"))
  push!(right_inds, leftindex(tn, site))
 
  site == Site(nsites(tn)) || push!(left_inds, rightindex(tn, site))
@@ -186,3 +186,35 @@ function canonize!(::Open, tn::Chain, site::Site; direction::Symbol, mode = :qr)
 
  return tn
 end
+
+mixed_canonize(tn::Chain, args...; kwargs...) = mixed_canonize!(deepcopy(tn), args...; kwargs...)
+mixed_canonize!(tn::Chain, args...; kwargs...) = mixed_canonize!(boundary(tn), tn, args...; kwargs...)
+
+"""
+ mixed_canonize!(boundary::Boundary, tn::Chain, center::Site)
+
+Transform a `Chain` tensor network into the mixed-canonical form, that is,
+for i < center the tensors are left-canonical and for i > center the tensors are right-canonical,
+and in the center there is a matrix with singular values.
+"""
+function mixed_canonize!(::Open, tn::Chain, center::Site) # TODO: center could be a range of sites
+ N = length(sites(tn))
+
+ # Left-to-right QR sweep -> get left-canonical tensors
+ for i in 1:N-1
+ canonize_site!(tn, Site(i); direction = :left, mode = :qr)
+ end
+
+ # Right-to-left QR sweep -> get left-canonical tensors for i > center
+ for i in N:-1:1
+ if i > center.id
+ canonize_site!(tn, Site(i); direction = :right, mode = :qr)
+ elseif i == center.id
+ canonize_site!(tn, Site(i); direction = :left, mode = :svd)
+ else
+ canonize_site!(tn, Site(i); direction = :left, mode = :qr)
+ end
+ end
+
+ return tn
+end

src/Qrochet.jl

@@ -17,7 +17,8 @@ export Product
 include("Ansatz/Chain.jl")
 export Chain
 export MPS, pMPS, MPO, pMPO
-export leftindex, rightindex, canonize, canonize!
+export leftindex, rightindex, canonize_site, canonize_site!
+export mixed_canonize, mixed_canonize!
 
 # reexports from Tenet
 using Tenet

test/Ansatz/Chain_test.jl

@@ -51,51 +51,68 @@
  @test rightsite(qtn, Site(1)) == Site(2)
  end
 
- @testset "canonize" begin
+ @testset "Canonization" begin
  using Tenet
 
  function is_left_canonical(qtn, s::Site)
- label_r = rightindex(qtn, s)
- A = select(qtn, :tensor, s)
- try
- contracted = contract(A, replace(conj(A), label_r => :new_ind_name))
- return isapprox(contracted, Matrix{Float64}(I, size(A, label_r), size(A, label_r)), atol=1e-12)
- catch
- return false
- end
- end
+  label_r = rightindex(qtn, s)
+  A = select(qtn, :tensor, s)
+  try
+  contracted = contract(A, replace(conj(A), label_r => :new_ind_name))
+  return isapprox(contracted, Matrix{Float64}(I, size(A, label_r), size(A, label_r)), atol=1e-12)
+  catch
+  return false
+  end
+  end
 
  function is_right_canonical(qtn, s::Site)
- label_l = leftindex(qtn, s)
- A = select(qtn, :tensor, s)
- try
- contracted = contract(A, replace(conj(A), label_l => :new_ind_name))
- return isapprox(contracted, Matrix{Float64}(I, size(A, label_l), size(A, label_l)), atol=1e-12)
- catch
- return false
- end
- end
-
- qtn = Chain(State(), Open(), [rand(4, 4), rand(4, 4, 4), rand(4, 4)])
-
- @test_throws ArgumentError canonize!(qtn, Site(1); direction=:right)
- @test_throws ArgumentError canonize!(qtn, Site(3); direction=:left)
-
- for mode in [:qr, :svd]
- for i in 1:length(sites(qtn))
- if i != 1
- canonized = canonize(qtn, Site(i); direction=:right, mode=mode)
- @test is_right_canonical(canonized, Site(i))
- @test isapprox(contract(transform(TensorNetwork(canonized), Tenet.HyperindConverter())), contract(TensorNetwork(qtn)))
- elseif i != length(sites(qtn))
- canonized = canonize(qtn, Site(i); direction=:left, mode=mode)
- @test is_left_canonical(canonized, Site(i))
- @test isapprox(contract(transform(TensorNetwork(canonized), Tenet.HyperindConverter())), contract(TensorNetwork(qtn)))
+ label_l = leftindex(qtn, s)
+ A = select(qtn, :tensor, s)
+ try
+ contracted = contract(A, replace(conj(A), label_l => :new_ind_name))
+ return isapprox(contracted, Matrix{Float64}(I, size(A, label_l), size(A, label_l)), atol=1e-12)
+ catch
+ return false
+ end
+ end
+
+ @testset "canonize_site" begin
+ qtn = Chain(State(), Open(), [rand(4, 4), rand(4, 4, 4), rand(4, 4)])
+
+ @test_throws ArgumentError canonize_site!(qtn, Site(1); direction=:right)
+ @test_throws ArgumentError canonize_site!(qtn, Site(3); direction=:left)
+
+ for mode in [:qr, :svd]
+ for i in 1:length(sites(qtn))
+ if i != 1
+ canonized = canonize_site(qtn, Site(i); direction=:right, mode=mode)
+ @test is_right_canonical(canonized, Site(i))
+ @test isapprox(contract(transform(TensorNetwork(canonized), Tenet.HyperindConverter())), contract(TensorNetwork(qtn)))
+ elseif i != length(sites(qtn))
+ canonized = canonize_site(qtn, Site(i); direction=:left, mode=mode)
+ @test is_left_canonical(canonized, Site(i))
+ @test isapprox(contract(transform(TensorNetwork(canonized), Tenet.HyperindConverter())), contract(TensorNetwork(qtn)))
+ end
  end
  end
+
+ # Ensure that svd creates a new tensor
+ @test length(tensors(canonize_site(qtn, Site(2); direction=:right, mode=:svd))) == 4
  end
 
- # Ensure that svd creates a new tensor
- @test length(tensors(canonize(qtn, Site(2); direction=:right, mode=:svd))) == 4
+ @testset "mixed_canonize" begin
+ qtn = Chain(State(), Open(), [rand(4, 4), rand(4, 4, 4), rand(4, 4, 4), rand(4, 4, 4), rand(4, 4)])
+ canonized = mixed_canonize(qtn, Site(3))
+
+ @test is_left_canonical(canonized, Site(1))
+ @test is_left_canonical(canonized, Site(2))
+ @test is_left_canonical(canonized, Site(3))
+ @test is_right_canonical(canonized, Site(4))
+ @test is_right_canonical(canonized, Site(5))
+
+ @test length(tensors(canonized)) == 6 # 5 tensors + 1 singular value matrix
+
+ @test isapprox(contract(transform(TensorNetwork(canonized), Tenet.HyperindConverter())), contract(TensorNetwork(qtn)))
+ end
  end
 end