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Yue-ZhengyuanYue-Zhengyuan
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Add NTU bond environments
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‎src/PEPSKit.jl‎

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@@ -58,6 +58,7 @@ include("algorithms/contractions/vumps_contractions.jl")
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include("algorithms/contractions/bondenv/benv_tools.jl")
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include("algorithms/contractions/bondenv/gaugefix.jl")
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include("algorithms/contractions/bondenv/als_solve.jl")
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include("algorithms/contractions/bondenv/benv_ntu.jl")
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include("algorithms/contractions/bondenv/benv_ctm.jl")
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include("algorithms/contractions/correlator/peps.jl")
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include("algorithms/contractions/correlator/pepo_1layer.jl")
@@ -104,6 +105,7 @@ export fixedpoint
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export absorb_weight
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export ALSTruncation, FullEnvTruncation
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export NNEnv, NNNEnv
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export su_iter, su3site_iter, simpleupdate, SimpleUpdate
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export InfiniteSquareNetwork

‎src/algorithms/contractions/bondenv/benv_ntu.jl‎

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#=
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The construction of bond environment for Neighborhood Tensor Update (NTU)
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is adapted from YASTN (https://github.com/yastn/yastn).
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Copyright 2024 The YASTN Authors. All Rights Reserved.
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Licensed under the Apache License, Version 2.0
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=#
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"""
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Algorithms to construct bond environment for Neighborhood Tensor Update (NTU).
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"""
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abstract type NeighbourEnv end
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"""
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Construct the "NTU-NN" bond environment.
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```
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(-1 +0)══(-1 +1)
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║ ║
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(+0 -1)═════X══ ═══Y═══(+0 +2)
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║ ║
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(+1 +0)══(+1 +1)
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```
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"""
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struct NNEnv <: NeighbourEnv end
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"""
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Calculate the bond environment within "NTU-NN" approximation.
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"""
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function bondenv_ntu(
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row::Int, col::Int, X::T, Y::T, state::S, alg::NNEnv
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) where {T <: StateTensor, S <: InfinitePEPS}
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neighbors = [(-1, 0), (0, -1), (1, 0), (1, 1), (0, 2), (-1, 1)]
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m = collect_neighbors(state, row, col, neighbors)
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#= contraction indices
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(-1 +0) ══ Dn ══ (-1 +1)
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║ ║
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........Dnw...... Dne
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║ : ║
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(+0 -1) ═══ X ══ Dw : De ══ Y ═══ (+0 +2)
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║ : ║
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Dsw :.......Dse........
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║ ║
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(+1 +0) ══ Ds ══ (+1 +1)
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=#
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# bottom-left half
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@autoopt @tensor benv_sw[Dse1 Dse0 Dw1 Dw0 Dnw1 Dnw0] :=
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cor_se(m[1, 1])[Dse1 Dse0 Ds1 Ds0] *
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cor_sw(m[1, 0])[Dsw1 Dsw0 Ds1 Ds0] *
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edge_w(X, hair_w(m[0, -1]))[Dnw1 Dnw0 Dw1 Dw0 Dsw1 Dsw0]
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normalize!(benv_sw, Inf)
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# top-right half
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@autoopt @tensor benv_ne[Dnw1 Dnw0 De1 De0 Dse1 Dse0] :=
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cor_nw(m[-1, 0])[Dn1 Dn0 Dnw1 Dnw0] *
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cor_ne(m[-1, 1])[Dne1 Dne0 Dn1 Dn0] *
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edge_e(Y, hair_e(m[0, 2]))[Dne1 Dne0 Dse1 Dse0 De1 De0]
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normalize!(benv_ne, Inf)
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@tensor benv[Dw1 De1; Dw0 De0] :=
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benv_sw[Dse1 Dse0 Dw1 Dw0 Dnw1 Dnw0] * benv_ne[Dnw1 Dnw0 De1 De0 Dse1 Dse0]
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normalize!(benv, Inf)
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return benv
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end
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"""
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Construct the "NTU-NN+" bond environment.
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```
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(-2 +0)┈┈(-2 +1)
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║ ║
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(-1 -1)┈(-1 +0)══(-1 +1)┈(-1 +2)
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┊ ║ ║ ┊
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(+0 -2)=(+0 -1)═════X══ ═══Y═══(+0 +2)=(+0 +3)
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┊ ║ ║ ┊
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(+1 -1)┈(+1 +0)══(+1 +1)┈(+1 +2)
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║ ║
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(+2 +0)┈┈(+2 +1)
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```
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The tensors connected with dotted lines (e.g. (-1 +2))
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are splitted into two hair tensors.
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"""
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struct NNpEnv <: NeighbourEnv end
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"""
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Calculate the bond environment within "NTU-NN+" approximation.
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"""
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function bondenv_ntu(
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row::Int, col::Int, X::T, Y::T, state::S, alg::NNpEnv
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) where {T <: StateTensor, S <: InfinitePEPS}
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neighbors = [
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(-1, -1), (0, -1), (1, -1), (1, 0), (1, 1), (1, 2), (0, 2), (-1, 2),
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(-1, 1), (-1, 0), (0, -2), (2, 0), (2, 1), (0, 3), (-2, 1), (-2, 0),
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]
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m = collect_neighbors(state, row, col, neighbors)
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error("To be implemented.")
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end
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"""
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Construct the "NTU-NNN" bond environment.
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```
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(-1 -1)=(-1 +0)══(-1 +1)=(-1 +2)
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║ ║ ║ ║
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(+0 -1)═════X══ ═══Y═══(+0 +2)
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║ ║ ║ ║
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(+1 -1)=(+1 +0)══(+1 +1)=(+1 +2)
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```
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"""
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struct NNNEnv <: NeighbourEnv end
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"""
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Calculates the bond environment within "NTU-NNN" approximation.
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"""
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function bondenv_ntu(
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row::Int, col::Int, X::T, Y::T, state::S, alg::NNNEnv
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) where {T <: StateTensor, S <: InfinitePEPS}
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neighbors = [
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(-1, -1), (0, -1), (1, -1),
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(1, 0), (1, 1), (1, 2), (0, 2),
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(-1, 2), (-1, 1), (-1, 0),
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]
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m = collect_neighbors(state, row, col, neighbors)
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#= left half
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(-1 -1)══════(-1 +0)═ -1/-2
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║ ║
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(+0 -1)════════ X ═══ -3/-4
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║ ║
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....D1..........D2.........
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║ ║
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(+1 -1)═ D3 ═(+1 +0)═ -5/-6
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=#
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vecl = enlarge_corner_nw(cor_nw(m[-1, -1]), edge_n(m[-1, 0]), edge_w(m[0, -1]), X)
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@tensor vecl[:] :=
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cor_sw(m[1, -1])[D11 D10 D31 D30] *
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edge_s(m[1, 0])[D21 D20 -5 -6 D31 D30] *
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vecl[D11 D10 D21 D20 -1 -2 -3 -4]
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normalize!(vecl, Inf)
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#= right half
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-1/-2 ══ (-1 +1)═ D1 ═(-1 +2)
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║ ║
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............D2..........D3...
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║ ║
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-3/-4 ═════ Y ═══════(+0 +2)
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║ ║
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-5/-6 ══ (+1 +1)═════(+1 +2)
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=#
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vecr = enlarge_corner_se(cor_se(m[1, 2]), edge_s(m[1, 1]), edge_e(m[0, 2]), Y)
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@tensor vecr[:] :=
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edge_n(m[-1, 1])[D11 D10 D21 D20 -1 -2] *
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cor_ne(m[-1, 2])[D31 D30 D11 D10] *
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vecr[D21 D20 D31 D30 -3 -4 -5 -6]
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normalize!(vecr, Inf)
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# combine left and right part
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@tensor benv[-1 -2; -3 -4] := vecl[1 2 -1 -3 3 4] * vecr[1 2 -2 -4 3 4]
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normalize!(benv, Inf)
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return benv
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end

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