Neighbourhood tensor update

Author: Yue-Zhengyuan

src/PEPSKit.jl

@@ -89,6 +89,7 @@ include("algorithms/contractions/bp_contractions.jl")
 include("algorithms/contractions/bondenv/benv_tools.jl")
 include("algorithms/contractions/bondenv/gaugefix.jl")
 include("algorithms/contractions/bondenv/als_solve.jl")
+include("algorithms/contractions/bondenv/benv_ntu.jl")
 include("algorithms/contractions/bondenv/benv_ctm.jl")
 include("algorithms/contractions/correlator/peps.jl")
 include("algorithms/contractions/correlator/pepo_1layer.jl")
@@ -111,6 +112,8 @@ include("algorithms/time_evolution/apply_mpo.jl")
 include("algorithms/time_evolution/time_evolve.jl")
 include("algorithms/time_evolution/simpleupdate.jl")
 include("algorithms/time_evolution/simpleupdate3site.jl")
+include("algorithms/time_evolution/ntupdate.jl")
+include("algorithms/time_evolution/ntupdate3site.jl")
 include("algorithms/time_evolution/gaugefix_su.jl")
 
 include("algorithms/bp/beliefpropagation.jl")
@@ -143,14 +146,16 @@ export fixedpoint
 
 export absorb_weight
 export ALSTruncation, FullEnvTruncation
-export SimpleUpdate
+export NNEnv, NNpEnv, NNNEnv
+export SimpleUpdate, NeighbourUpdate
 export TimeEvolver, timestep, time_evolve
 
 export InfiniteSquareNetwork
 export InfinitePartitionFunction
 export InfinitePEPS, InfiniteTransferPEPS
 export SUWeight
 export InfinitePEPO, InfiniteTransferPEPO
+export infinite_temperature_density_matrix
 
 export BPEnv, BeliefPropagation
 export BPGauge, SUGauge

src/algorithms/contractions/bondenv/benv_ntu.jl

@@ -0,0 +1,239 @@
+#= 
+The construction of bond environment for Neighborhood Tensor Update (NTU) 
+is adapted from YASTN (https://github.com/yastn/yastn).
+Copyright 2024 The YASTN Authors. All Rights Reserved.
+Licensed under the Apache License, Version 2.0
+=#
+
+"""
+Algorithms to construct bond environment for Neighborhood Tensor Update (NTU).
+"""
+abstract type NeighbourEnv end
+
+"""
+SVD with `truncrank(1)`.
+"""
+function _svd_cut!(t::AbstractTensorMap)
+    t1, s, t2 = svd_trunc!(t; trunc = truncrank(1))
+    return absorb_s(t1, s, t2)
+end
+
+"""
+Algorithm struct for "NTU-NN" bond environment. 
+"""
+struct NNEnv <: NeighbourEnv end
+"""
+Calculate the bond environment within "NTU-NN" approximation.
+```
+    -1      ●=======●
+            ║       ║
+    0   ●===X==   ==Y===●
+            ║       ║
+    1       ●=======●
+        -1  0       1   2
+```
+"""
+function bondenv_ntu(
+        row::Int, col::Int, X::T, Y::T, state::S, alg::NNEnv
+    ) where {T, S <: InfiniteState}
+    neighbors = [(-1, 0), (0, -1), (1, 0), (1, 1), (0, 2), (-1, 1)]
+    m = collect_neighbors(state, row, col, neighbors)
+    X, Y = _prepare_site_tensor(X), _prepare_site_tensor(Y)
+    # southwest half
+    @autoopt @tensor benv_sw[Dse1 Dse0 Dw1 Dw0 Dnw1 Dnw0] :=
+        cor_se(m[1, 1])[Dse1 Dse0 Ds1 Ds0] *
+        cor_sw(m[1, 0])[Dsw1 Dsw0 Ds1 Ds0] *
+        edge_w(X, hair_w(m[0, -1]))[Dnw1 Dnw0 Dw1 Dw0 Dsw1 Dsw0]
+    normalize!(benv_sw, Inf)
+    # northeast half
+    @autoopt @tensor benv_ne[Dnw1 Dnw0 De1 De0 Dse1 Dse0] :=
+        cor_nw(m[-1, 0])[Dn1 Dn0 Dnw1 Dnw0] *
+        cor_ne(m[-1, 1])[Dne1 Dne0 Dn1 Dn0] *
+        edge_e(Y, hair_e(m[0, 2]))[Dne1 Dne0 Dse1 Dse0 De1 De0]
+    normalize!(benv_ne, Inf)
+    @tensor benv[Dw1 De1; Dw0 De0] :=
+        benv_sw[Dse1 Dse0 Dw1 Dw0 Dnw1 Dnw0] * benv_ne[Dnw1 Dnw0 De1 De0 Dse1 Dse0]
+    normalize!(benv, Inf)
+    return benv
+end
+
+"""
+Algorithm struct for "NTU-NN+" bond environment. 
+"""
+struct NNpEnv <: NeighbourEnv end
+"""
+Calculate the bond environment within "NTU-NN+" approximation.
+```
+    -2          ●.......●
+                ║       ║
+    -1      ○===●=======●===○
+            ║   ║       ║   ║
+    0   ●===●===X==   ==Y===●===●
+            ║   ║       ║   ║
+    1       ○===●=======●===○
+                ║       ║
+    2           ●.......●
+        -2  -1  0       1   2   3
+```
+Dotted lines and ○ are splitted using SVD with `truncrank(1)`.
+"""
+function bondenv_ntu(
+        row::Int, col::Int, X::T, Y::T, state::S, alg::NNpEnv
+    ) where {T, S <: InfiniteState}
+    neighbors = [
+        (-1, -1), (0, -1), (1, -1), (1, 0), (1, 1), (1, 2), (0, 2), (-1, 2),
+        (-1, 1), (-1, 0), (0, -2), (2, 0), (2, 1), (0, 3), (-2, 1), (-2, 0),
+    ]
+    ms = collect_neighbors(state, row, col, neighbors)
+    X, Y = _prepare_site_tensor(X), _prepare_site_tensor(Y)
+
+    # ---- hairs (size D^2) with a 1D auxiliary leg ----
+
+    @tensor top[-1 -2; -3 -4] := cor_nw(ms[-2, 0])[1 2 -1 -2] * cor_ne(ms[-2, 1])[-3 -4 1 2]
+    tl, tr = _svd_cut!(top)
+
+    @tensor bot[-1 -2; -3 -4] := cor_sw(ms[2, 0])[-1 -2 1 2] * cor_se(ms[2, 1])[-3 -4 1 2]
+    bl, br = _svd_cut!(bot)
+
+    nw = permute(cor_nw(ms[-1, -1]), ((3, 4), (1, 2)))
+    nw1, nw2 = _svd_cut!(nw)
+
+    ne = permute(cor_ne(ms[-1, 2]), ((3, 4), (1, 2)))
+    ne1, ne2 = _svd_cut!(ne)
+
+    sw = permute(cor_sw(ms[1, -1]), ((1, 2), (3, 4)))
+    sw1, sw2 = _svd_cut!(sw)
+
+    se = permute(cor_se(ms[1, 2]), ((3, 4), (1, 2)))
+    se1, se2 = _svd_cut!(se)
+
+    m = ms[0, -1]
+    @tensoropt hW[anw DXw1 DXw0 asw] :=
+        hair_w(ms[0, -2])[Dw21 Dw20] *
+        nw1[Dnw11 Dnw10 anw] * sw1[Dsw11 Dsw10 asw] *
+        twistdual(m, 1)[p Dnw10 DXw0 Dsw10 Dw20] *
+        conj(m[p Dnw11 DXw1 Dsw11 Dw21])
+
+    m = ms[0, 2]
+    @tensoropt hE[ane DYe1 DYe0 ase] :=
+        hair_e(ms[0, 3])[De21 De20] *
+        ne2[ane Dne21 Dne20] * se2[ase Dse21 Dse20] *
+        twistdual(m, 1)[p Dne20 De20 Dse20 DYe0] *
+        conj(m[p Dne21 De21 Dse21 DYe1])
+
+    # ---- corners (size D^4) with a 1D auxiliary leg ----
+
+    m = ms[-1, 0]
+    @tensoropt NW[at Dn1 Dn0 DXn1 DXn0 anw] :=
+        tl[Dtl1 Dtl0 at] * nw2[anw Dnw21 Dnw20] *
+        twistdual(m, 1)[p Dtl0 Dn0 DXn0 Dnw20] *
+        conj(m[p Dtl1 Dn1 DXn1 Dnw21])
+
+    m = ms[-1, 1]
+    @tensoropt NE[at Dn1 Dn0 DYn1 DYn0 ane] :=
+        tr[at Dtr1 Dtr0] * ne1[Dne11 Dne10 ane] *
+        twistdual(m, 1)[p Dtr0 Dne10 DYn0 Dn0] *
+        conj(m[p Dtr1 Dne11 DYn1 Dn1])
+
+    m = ms[1, 0]
+    @tensoropt SW[asw DXs1 DXs0 Ds1 Ds0 ab] :=
+        bl[Dbl1 Dbl0 ab] * sw2[asw Dsw21 Dsw20] *
+        twistdual(m, 1)[p DXs0 Ds0 Dbl0 Dsw20] *
+        conj(m[p DXs1 Ds1 Dbl1 Dsw21])
+
+    m = ms[1, 1]
+    @tensoropt SE[ase DYs1 DYs0 Ds1 Ds0 ab] :=
+        br[ab Dbr1 Dbr0] * se1[Dse11 Dse10 ase] *
+        twistdual(m, 1)[p DYs0 Dse10 Dbr0 Ds0] *
+        conj(m[p DYs1 Dse11 Dbr1 Ds1])
+
+    # ---- left half ----
+    @tensoropt benvL[at Dn1 Dn0 Dw1 Dw0 Ds1 Ds0 ab] :=
+        hW[anw DXw1 DXw0 asw] *
+        NW[at Dn1 Dn0 DXn1 DXn0 anw] *
+        SW[asw DXs1 DXs0 Ds1 Ds0 ab] *
+        twistdual(X, 1)[p DXn0 Dw0 DXs0 DXw0] *
+        conj(X[p DXn1 Dw1 DXs1 DXw1])
+    normalize!(benvL, Inf)
+
+    # ---- right half ----
+
+    @tensoropt benvR[at Dn1 Dn0 De1 De0 Ds1 Ds0 ab] :=
+        hE[ane DYe1 DYe0 ase] *
+        NE[at Dn1 Dn0 DYn1 DYn0 ane] *
+        SE[ase DYs1 DYs0 Ds1 Ds0 ab] *
+        twistdual(Y, 1)[p DYn0 DYe0 DYs0 De0] *
+        conj(Y[p DYn1 DYe1 DYs1 De1])
+    normalize!(benvR, Inf)
+
+    # ---- the full NN+ environment ----
+
+    @tensor benv[Dw1, De1; Dw0, De0] :=
+        benvL[at Dn1 Dn0 Dw1 Dw0 Ds1 Ds0 ab] *
+        benvR[at Dn1 Dn0 De1 De0 Ds1 Ds0 ab]
+    normalize!(benv, Inf)
+    return benv
+end
+
+"""
+Algorithm struct for "NTU-NNN" bond environment. 
+"""
+struct NNNEnv <: NeighbourEnv end
+"""
+Calculates the bond environment within "NTU-NNN" approximation.
+```
+    -1  ●===●=======●===●
+        ║   ║       ║   ║
+    0   ●===X==   ==Y===●
+        ║   ║       ║   ║
+    1   ●===●=======●===●
+        -1  0       1   2
+```
+"""
+function bondenv_ntu(
+        row::Int, col::Int, X::T, Y::T, state::S, alg::NNNEnv
+    ) where {T, S <: InfiniteState}
+    neighbors = [
+        (-1, -1), (0, -1), (1, -1),
+        (1, 0), (1, 1), (1, 2), (0, 2),
+        (-1, 2), (-1, 1), (-1, 0),
+    ]
+    m = collect_neighbors(state, row, col, neighbors)
+    X, Y = _prepare_site_tensor(X), _prepare_site_tensor(Y)
+    #= left half
+    -1  ●======●=== -1/-2
+        ║      ║
+    0   ●======X=== -3/-4
+        ║      ║
+    ....D1.....D2...
+        ║      ║
+    1   ●==D3==●=== -5/-6
+        -1     0
+    =#
+    vecl = enlarge_corner_nw(cor_nw(m[-1, -1]), edge_n(m[-1, 0]), edge_w(m[0, -1]), X)
+    @tensor vecl[:] :=
+        cor_sw(m[1, -1])[D11 D10 D31 D30] *
+        edge_s(m[1, 0])[D21 D20 -5 -6 D31 D30] *
+        vecl[D11 D10 D21 D20 -1 -2 -3 -4]
+    normalize!(vecl, Inf)
+    #= right half
+    -1  -1/-2===●==D1==●
+                ║      ║
+        ........D2.....D3...
+                ║      ║
+    0   -3/-4===Y======●
+                ║      ║     
+    1   -5/-6===●======●
+                0      1
+    =#
+    vecr = enlarge_corner_se(cor_se(m[1, 2]), edge_s(m[1, 1]), edge_e(m[0, 2]), Y)
+    @tensor vecr[:] :=
+        edge_n(m[-1, 1])[D11 D10 D21 D20 -1 -2] *
+        cor_ne(m[-1, 2])[D31 D30 D11 D10] *
+        vecr[D21 D20 D31 D30 -3 -4 -5 -6]
+    normalize!(vecr, Inf)
+    # combine left and right part
+    @tensor benv[-1 -2; -3 -4] := vecl[1 2 -1 -3 3 4] * vecr[1 2 -2 -4 3 4]
+    normalize!(benv, Inf)
+    return benv
+end