Correlator for purified iPEPO and right-to-left contraction

docs/src/changelog.md

@@ -24,6 +24,8 @@ When releasing a new version, move the "Unreleased" changes to a new version sec
 
 ### Changed
 
+- In `correlator`, sites `js` are allowed on either side of the reference site `i` by adding right-to-left contractions (#399)
+
 ### Deprecated
 
 ### Removed

src/PEPSKit.jl

@@ -96,6 +96,7 @@ include("algorithms/contractions/bondenv/gaugefix.jl")
 include("algorithms/contractions/bondenv/als_solve.jl")
 include("algorithms/contractions/bondenv/benv_ctm.jl")
 include("algorithms/contractions/correlator/peps.jl")
+include("algorithms/contractions/correlator/pepo_purified.jl")
 include("algorithms/contractions/correlator/pepo_1layer.jl")
 
 include("algorithms/ctmrg/sparse_environments.jl")
@@ -126,6 +127,7 @@ include("algorithms/bp/gaugefix.jl")
 
 include("algorithms/transfermatrix.jl")
 include("algorithms/toolbox.jl")
+include("algorithms/correlator_adapters.jl")
 include("algorithms/correlators.jl")
 
 include("algorithms/optimization/fixed_point_differentiation.jl")

src/algorithms/contractions/correlator/pepo_1layer.jl

@@ -1,4 +1,6 @@
-function start_correlator(
+# -------- For left-to-right correlator contraction --------
+
+function start_correlator_left(
         i::CartesianIndex{2}, ρ::InfinitePEPO,
         O::PFTensor, env::CTMRGEnv
     )
@@ -25,8 +27,8 @@ function start_correlator(
     return Vn, Vo
 end
 
-function end_correlator_numerator(
-        j::CartesianIndex{2}, V::CTMRGEdgeTensor{T, S, 3},
+function end_correlator_right_numerator(
+        j::CartesianIndex{2}, V::AbstractTensorMap{T, S, 3, 1},
         ρ::InfinitePEPO, O::PFTensor, env::CTMRGEnv
     ) where {T, S}
     (size(ρ, 3) == 1) ||
@@ -44,8 +46,8 @@ function end_correlator_numerator(
         t[d1 d2; DN DE DS DW] * removeunit(O, 4)[dstring d2; d1]
 end
 
-function end_correlator_denominator(
-        j::CartesianIndex{2}, V::CTMRGEdgeTensor{T, S, 2}, env::CTMRGEnv
+function end_correlator_right_denominator(
+        j::CartesianIndex{2}, V::AbstractTensorMap{T, S, 2, 1}, env::CTMRGEnv
     ) where {T, S}
     r, c = Tuple(j)
     C_northeast = corner(env, NORTHEAST, r - 1, c + 1)
@@ -54,3 +56,62 @@ function end_correlator_denominator(
     return @autoopt @tensor V[χS DE; χN] * C_northeast[χN; χNE] *
         E_east[χNE DE; χSE] * C_southeast[χSE; χS]
 end
+
+# -------- For right-to-left correlator contraction --------
+
+function start_correlator_right(
+        i::CartesianIndex{2}, ρ::InfinitePEPO,
+        O::PFTensor, env::CTMRGEnv
+    )
+    (size(ρ, 3) == 1) ||
+        throw(ArgumentError("The input PEPO ρ must have only one layer."))
+    r, c = Tuple(i)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_east = edge(env, EAST, r, c + 1)
+    E_south = edge(env, SOUTH, r + 1, c)
+    C_northeast = corner(env, NORTHEAST, r - 1, c + 1)
+    C_southeast = corner(env, SOUTHEAST, r + 1, c + 1)
+    t = twistdual(ρ[r, c], 1:2)
+    @autoopt @tensor Vn[χNW DW; χSW] :=
+        E_south[χSSE DS; χSW] * E_east[χNEE DE; χSEE] *
+        E_north[χNW DN; χNNE] * C_northeast[χNNE; χNEE] *
+        C_southeast[χSEE; χSSE] * t[d d; DN DE DS DW]
+    @autoopt @tensor Vo[χNW DW dstring; χSW] :=
+        E_south[χSSE DS; χSW] * E_east[χNEE DE; χSEE] *
+        E_north[χNW DN; χNNE] * C_northeast[χNNE; χNEE] *
+        C_southeast[χSEE; χSSE] *
+        removeunit(O, 1)[d2; d1 dstring] * t[d1 d2; DN DE DS DW]
+    return Vn, Vo
+end
+
+
+function end_correlator_left_numerator(
+        j::CartesianIndex{2}, V::AbstractTensorMap{T, S, 3, 1},
+        ρ::InfinitePEPO, O::PFTensor, env::CTMRGEnv
+    ) where {T, S}
+    (size(ρ, 3) == 1) ||
+        throw(ArgumentError("The input PEPO ρ must have only one layer."))
+    r, c = Tuple(j)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_south = edge(env, SOUTH, r + 1, c)
+    E_west = edge(env, WEST, r, c - 1)
+    C_northwest = corner(env, NORTHWEST, r - 1, c - 1)
+    C_southwest = corner(env, SOUTHWEST, r + 1, c - 1)
+    t = twistdual(ρ[r, c], 1:2)
+    return @autoopt @tensor V[χNE DE dstring; χSE] *
+        E_south[χSE DS; χSW2] * C_southwest[χSW2; χSW] *
+        E_west[χSW DW; χNW] * C_northwest[χNW; χN] *
+        E_north[χN DN; χNE] *
+        t[d1 d2; DN DE DS DW] * removeunit(O, 4)[dstring d2; d1]
+end
+
+function end_correlator_left_denominator(
+        j::CartesianIndex{2}, V::AbstractTensorMap{T, S, 2, 1}, env::CTMRGEnv
+    ) where {T, S}
+    r, c = Tuple(j)
+    C_northwest = corner(env, NORTHWEST, r - 1, c - 1)
+    E_west = edge(env, WEST, r, c - 1)
+    C_southwest = corner(env, SOUTHWEST, r + 1, c - 1)
+    return @autoopt @tensor V[χN DE; χS] * C_southwest[χS; χSW] *
+        E_west[χSW DE; χNW] * C_northwest[χNW; χN]
+end

src/algorithms/contractions/correlator/pepo_purified.jl

@@ -0,0 +1,135 @@
+# -------- For left-to-right correlator contraction --------
+
+function start_correlator_left(
+        i::CartesianIndex{2},
+        below::InfinitePEPO,
+        O::MPOTensor,
+        above::InfinitePEPO,
+        env::CTMRGEnv,
+    )
+    r, c = Tuple(i)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_south = edge(env, SOUTH, r + 1, c)
+    E_west = edge(env, WEST, r, c - 1)
+    C_northwest = corner(env, NORTHWEST, r - 1, c - 1)
+    C_southwest = corner(env, SOUTHWEST, r + 1, c - 1)
+    ket = twistdual(below[r, c], (1, 2))
+    bra = above[r, c]
+
+    @autoopt @tensor Vn[χSE Detop Debot; χNE] :=
+        E_south[χSE Dstop Dsbot; χSW2] *
+        C_southwest[χSW2; χSW] *
+        E_west[χSW Dwtop Dwbot; χNW] *
+        C_northwest[χNW; χN] *
+        conj(bra[d a; Dnbot Debot Dsbot Dwbot]) *
+        ket[d a; Dntop Detop Dstop Dwtop] *
+        E_north[χN Dntop Dnbot; χNE]
+
+    @autoopt @tensor Vo[χSE Detop dstring Debot; χNE] :=
+        E_south[χSE Dstop Dsbot; χSW2] *
+        C_southwest[χSW2; χSW] *
+        E_west[χSW Dwtop Dwbot; χNW] *
+        C_northwest[χNW; χN] *
+        conj(bra[d1 a; Dnbot Debot Dsbot Dwbot]) *
+        removeunit(O, 1)[d1; d2 dstring] *
+        ket[d2 a; Dntop Detop Dstop Dwtop] *
+        E_north[χN Dntop Dnbot; χNE]
+
+    return Vn, Vo
+end
+
+function end_correlator_right_numerator(
+        j::CartesianIndex{2},
+        V::AbstractTensorMap{T, S, 4, 1},
+        above::InfinitePEPO,
+        O::MPOTensor,
+        below::InfinitePEPO,
+        env::CTMRGEnv,
+    ) where {T, S}
+    r, c = Tuple(j)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_east = edge(env, EAST, r, c + 1)
+    E_south = edge(env, SOUTH, r + 1, c)
+    C_northeast = corner(env, NORTHEAST, r - 1, c + 1)
+    C_southeast = corner(env, SOUTHEAST, r + 1, c + 1)
+    ket = twistdual(above[r, c], (1, 2))
+    bra = below[r, c]
+
+    return @autoopt @tensor V[χSW DWt dstring DWb; χNW] *
+        E_south[χSSE DSt DSb; χSW] *
+        E_east[χNEE DEt DEb; χSEE] *
+        E_north[χNW DNt DNb; χNNE] *
+        C_northeast[χNNE; χNEE] *
+        C_southeast[χSEE; χSSE] *
+        conj(bra[db a; DNb DEb DSb DWb]) *
+        ket[dt a; DNt DEt DSt DWt] *
+        removeunit(O, 4)[dstring db; dt]
+end
+
+# -------- For right-to-left correlator contraction --------
+
+function start_correlator_right(
+        i::CartesianIndex{2},
+        below::InfinitePEPO,
+        O::MPOTensor,
+        above::InfinitePEPO,
+        env::CTMRGEnv,
+    )
+    r, c = Tuple(i)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_east = edge(env, EAST, r, c + 1)
+    E_south = edge(env, SOUTH, r + 1, c)
+    C_northeast = corner(env, NORTHEAST, r - 1, c + 1)
+    C_southeast = corner(env, SOUTHEAST, r + 1, c + 1)
+    ket = twistdual(below[r, c], (1, 2))
+    bra = above[r, c]
+
+    @autoopt @tensor Vn[χNW DWtop DWbot; χSW] :=
+        E_south[χSSE Dstop Dsbot; χSW] *
+        E_east[χNEE Detop Debot; χSEE] *
+        E_north[χNW Dntop Dnbot; χNNE] *
+        C_northeast[χNNE; χNEE] *
+        C_southeast[χSEE; χSSE] *
+        conj(bra[d a; Dnbot Debot Dsbot DWbot]) *
+        ket[d a; Dntop Detop Dstop DWtop]
+
+    @autoopt @tensor Vo[χNW DWtop dstring DWbot; χSW] :=
+        E_south[χSSE Dstop Dsbot; χSW] *
+        E_east[χNEE Detop Debot; χSEE] *
+        E_north[χNW Dntop Dnbot; χNNE] *
+        C_northeast[χNNE; χNEE] *
+        C_southeast[χSEE; χSSE] *
+        conj(bra[d1 a; Dnbot Debot Dsbot DWbot]) *
+        removeunit(O, 1)[d1; d2 dstring] *
+        ket[d2 a; Dntop Detop Dstop DWtop]
+
+    return Vn, Vo
+end
+
+function end_correlator_left_numerator(
+        j::CartesianIndex{2},
+        V::AbstractTensorMap{T, S, 4, 1},
+        above::InfinitePEPO,
+        O::MPOTensor,
+        below::InfinitePEPO,
+        env::CTMRGEnv,
+    ) where {T, S}
+    r, c = Tuple(j)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_south = edge(env, SOUTH, r + 1, c)
+    E_west = edge(env, WEST, r, c - 1)
+    C_northwest = corner(env, NORTHWEST, r - 1, c - 1)
+    C_southwest = corner(env, SOUTHWEST, r + 1, c - 1)
+    ket = twistdual(above[r, c], (1, 2))
+    bra = below[r, c]
+
+    return @autoopt @tensor V[χNE DEt dstring DEb; χSE] *
+        E_south[χSE DSt DSb; χSW2] *
+        C_southwest[χSW2; χSW] *
+        E_west[χSW DWt DWb; χNW] *
+        C_northwest[χNW; χN] *
+        E_north[χN DNt DNb; χNE] *
+        conj(bra[db a; DNb DEb DSb DWb]) *
+        ket[dt a; DNt DEt DSt DWt] *
+        removeunit(O, 4)[dstring db; dt]
+end

src/algorithms/contractions/correlator/peps.jl

@@ -1,4 +1,6 @@
-function start_correlator(
+# -------- For left-to-right correlator contraction --------
+
+function start_correlator_left(
         i::CartesianIndex{2},
         below::InfinitePEPS,
         O::MPOTensor,
@@ -37,7 +39,7 @@ function start_correlator(
     return Vn, Vo
 end
 
-function end_correlator_numerator(
+function end_correlator_right_numerator(
         j::CartesianIndex{2},
         V::AbstractTensorMap{T, S, 4, 1},
         above::InfinitePEPS,
@@ -64,7 +66,7 @@ function end_correlator_numerator(
         removeunit(O, 4)[dstring db; dt]
 end
 
-function end_correlator_denominator(
+function end_correlator_right_denominator(
         j::CartesianIndex{2}, V::AbstractTensorMap{T, S, 3, 1},
         env::CTMRGEnv
     ) where {T, S}
@@ -78,3 +80,84 @@ function end_correlator_denominator(
         E_east[χNE DEt DEb; χSE] *
         C_southeast[χSE; χS]
 end
+
+# -------- For right-to-left correlator contraction --------
+
+function start_correlator_right(
+        i::CartesianIndex{2},
+        below::InfinitePEPS,
+        O::MPOTensor,
+        above::InfinitePEPS,
+        env::CTMRGEnv,
+    )
+    r, c = Tuple(i)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_east = edge(env, EAST, r, c + 1)
+    E_south = edge(env, SOUTH, r + 1, c)
+    C_northeast = corner(env, NORTHEAST, r - 1, c + 1)
+    C_southeast = corner(env, SOUTHEAST, r + 1, c + 1)
+    sandwich = (below[r, c], above[r, c])
+
+    @autoopt @tensor Vn[χNW DWtop DWbot; χSW] :=
+        E_south[χSSE Dstop Dsbot; χSW] *
+        E_east[χNEE Detop Debot; χSEE] *
+        E_north[χNW Dntop Dnbot; χNNE] *
+        C_northeast[χNNE; χNEE] *
+        C_southeast[χSEE; χSSE] *
+        conj(bra(sandwich)[d; Dnbot Debot Dsbot DWbot]) *
+        ket(sandwich)[d; Dntop Detop Dstop DWtop]
+
+    @autoopt @tensor Vo[χNW DWtop dstring DWbot; χSW] :=
+        E_south[χSSE Dstop Dsbot; χSW] *
+        E_east[χNEE Detop Debot; χSEE] *
+        E_north[χNW Dntop Dnbot; χNNE] *
+        C_northeast[χNNE; χNEE] *
+        C_southeast[χSEE; χSSE] *
+        conj(bra(sandwich)[d1; Dnbot Debot Dsbot DWbot]) *
+        removeunit(O, 1)[d1; d2 dstring] *
+        ket(sandwich)[d2; Dntop Detop Dstop DWtop]
+
+    return Vn, Vo
+end
+
+function end_correlator_left_numerator(
+        j::CartesianIndex{2},
+        V::AbstractTensorMap{T, S, 4, 1},
+        above::InfinitePEPS,
+        O::MPOTensor,
+        below::InfinitePEPS,
+        env::CTMRGEnv,
+    ) where {T, S}
+    r, c = Tuple(j)
+    E_north = edge(env, NORTH, r - 1, c)
+    E_south = edge(env, SOUTH, r + 1, c)
+    E_west = edge(env, WEST, r, c - 1)
+    C_northwest = corner(env, NORTHWEST, r - 1, c - 1)
+    C_southwest = corner(env, SOUTHWEST, r + 1, c - 1)
+    sandwich = (above[r, c], below[r, c])
+
+    return @autoopt @tensor V[χNE DEt dstring DEb; χSE] *
+        E_south[χSE DSt DSb; χSW2] *
+        C_southwest[χSW2; χSW] *
+        E_west[χSW DWt DWb; χNW] *
+        C_northwest[χNW; χN] *
+        E_north[χN DNt DNb; χNE] *
+        conj(bra(sandwich)[db; DNb DEb DSb DWb]) *
+        ket(sandwich)[dt; DNt DEt DSt DWt] *
+        removeunit(O, 4)[dstring db; dt]
+end
+
+function end_correlator_left_denominator(
+        j::CartesianIndex{2}, V::AbstractTensorMap{T, S, 3, 1},
+        env::CTMRGEnv
+    ) where {T, S}
+    r, c = Tuple(j)
+    C_northwest = corner(env, NORTHWEST, r - 1, c - 1)
+    E_west = edge(env, WEST, r, c - 1)
+    C_southwest = corner(env, SOUTHWEST, r + 1, c - 1)
+
+    return @autoopt @tensor V[χN DEt DEb; χS] *
+        C_southwest[χS; χSW] *
+        E_west[χSW DEt DEb; χNW] *
+        C_northwest[χNW; χN]
+end