Rewrite local expectation values as a single contraction

src/operators/localoperator.jl

@@ -35,7 +35,7 @@
 
 function operator_env(peps::InfinitePEPS, env::CTMRGEnv, ::OnSite)
     return map(Iterators.product(axes(env.corners, 2), axes(env.corners, 3))) do (r, c)
-        @tensor ρ[-1; -2] :=
+        @tensor opt = true ρ[-1; -2] :=
             env.corners[NORTHWEST, r, c][1; 2] *
             env.edges[NORTH, r, c][2 3 4; 5] *
             env.corners[NORTHEAST, r, c][5; 6] *
@@ -52,7 +52,7 @@
 function operator_env(peps::InfinitePEPS, env::CTMRGEnv, ::NearestNeighbor)
     return map(Iterators.product(axes(env.corners, 2), axes(env.corners, 3))) do (r, c)
         cnext = _next(c, size(peps, 2))
-        @tensor ρ[-11 -20; -12 -18] :=
+        @tensor opt = true ρ[-12 -18; -11 -20] :=
             env.corners[NORTHWEST, r, c][1; 3] *
             env.edges[NORTH, r, c][3 5 8; 13] *
             env.edges[NORTH, r, cnext][13 16 22; 23] *
@@ -77,21 +77,140 @@
 of `peps` and `env`.
 """ MPSKit.expectation_value(::InfinitePEPS, ::Any, ::NLocalOperator)
 
+# Optimal contraction order is obtained by manually trying out some space sizes and using costcheck = warn
+# in principle, we would like to use opt = true, but this does not give optimal results without also supplying costs
+# However, due to a bug in tensoroperations this is currently not possible with integer labels.
+# Thus, this is a workaround until the bug is fixed. (otherwise we'd need to rewrite all the labels to symbols...)
+
 # 1-site operator expectation values on unit cell
-function MPSKit.expectation_value(peps::InfinitePEPS, env, O::NLocalOperator{OnSite})
-    return map(operator_env(peps, env, OnSite())) do ρ
-        o = @tensor ρ[-1; -2] * O.op[-1; -2]
-        n = @tensor ρ[-1; -1]
+function MPSKit.expectation_value(
+    peps::InfinitePEPS, env::CTMRGEnv, O::NLocalOperator{OnSite}
+)
+    return map(Iterators.product(axes(env.corners, 2), axes(env.corners, 3))) do (r, c)
+        o = @tensor order = (6, 2, 5, 10, 14, 13, 11, 15, 7, 9, 1, 3, 4, 8, 12, 16, 18, 17) begin
+            env.corners[NORTHWEST, r, c][1; 2] *
+            env.edges[NORTH, r, c][2 3 4; 5] *
+            env.corners[NORTHEAST, r, c][5; 6] *
+            env.edges[EAST, r, c][6 7 8; 9] *
+            env.corners[SOUTHEAST, r, c][9; 10] *
+            env.edges[SOUTH, r, c][10 11 12; 13] *
+            env.corners[SOUTHWEST, r, c][13; 14] *
+            env.edges[WEST, r, c][14 15 16; 1] *
+            peps[r, c][17; 3 7 11 15] *
+            conj(peps[r, c][18; 4 8 12 16]) *
+            O.op[18; 17]
+        end
+        n = @tensor order = (9, 13, 10, 5, 1, 2, 4, 16, 6, 8, 14, 12, 17, 3, 7, 11, 15) begin
+            env.corners[NORTHWEST, r, c][1; 2] *
+            env.edges[NORTH, r, c][2 3 4; 5] *
+            env.corners[NORTHEAST, r, c][5; 6] *
+            env.edges[EAST, r, c][6 7 8; 9] *
+            env.corners[SOUTHEAST, r, c][9; 10] *
+            env.edges[SOUTH, r, c][10 11 12; 13] *
+            env.corners[SOUTHWEST, r, c][13; 14] *
+            env.edges[WEST, r, c][14 15 16; 1] *
+            peps[r, c][17; 3 7 11 15] *
+            conj(peps[r, c][17; 4 8 12 16])
+        end
         o / n
     end
 end
 
 function MPSKit.expectation_value(
     peps::InfinitePEPS, env, O::NLocalOperator{NearestNeighbor}
 )
-    return map(operator_env(peps, env, NearestNeighbor())) do ρ
-        o = @tensor ρ[1 2; 3 4] * O.op[1 2; 3 4]
-        n = @tensor ρ[1 2; 1 2]
+    return map(Iterators.product(axes(env.corners, 2), axes(env.corners, 3))) do (r, c)
+        cnext = _next(c, size(peps, 2))
+        o = @tensor order = (
+            28,
+            24,
+            23,
+            16,
+            25,
+            22,
+            26,
+            27,
+            17,
+            21,
+            4,
+            1,
+            3,
+            5,
+            7,
+            8,
+            9,
+            2,
+            6,
+            10,
+            14,
+            19,
+            15,
+            13,
+            31,
+            32,
+            29,
+            30,
+        ) begin # physical spaces
+            env.corners[NORTHWEST, r, c][1; 3] *
+            env.edges[NORTH, r, c][3 5 8; 13] *
+            env.edges[NORTH, r, cnext][13 16 22; 23] *
+            env.corners[NORTHEAST, r, cnext][23; 24] *
+            env.edges[EAST, r, cnext][24 25 26; 27] *
+            env.corners[SOUTHEAST, r, cnext][27; 28] *
+            env.edges[SOUTH, r, cnext][28 17 21; 14] *
+            env.edges[SOUTH, r, c][14 6 10; 4] *
+            env.corners[SOUTHWEST, r, c][4; 2] *
+            env.edges[WEST, r, c][2 7 9; 1] *
+            peps[r, c][29; 5 15 6 7] *
+            conj(peps[r, c][31; 8 19 10 9]) *
+            peps[r, cnext][30; 16 25 17 15] *
+            conj(peps[r, cnext][32; 22 26 21 19]) *
+            O.op[31 32; 29 30]
+        end
+
+        n = @tensor order = (
+            2,
+            3,
+            1,
+            5,
+            7,
+            28,
+            24,
+            23,
+            16,
+            25,
+            30,
+            22,
+            26,
+            27,
+            17,
+            21,
+            14,
+            15,
+            6,
+            4,
+            13,
+            29,
+            8,
+            19,
+            10,
+            9,
+        ) begin
+            env.corners[NORTHWEST, r, c][1; 3] *
+            env.edges[NORTH, r, c][3 5 8; 13] *
+            env.edges[NORTH, r, cnext][13 16 22; 23] *
+            env.corners[NORTHEAST, r, cnext][23; 24] *
+            env.edges[EAST, r, cnext][24 25 26; 27] *
+            env.corners[SOUTHEAST, r, cnext][27; 28] *
+            env.edges[SOUTH, r, cnext][28 17 21; 14] *
+            env.edges[SOUTH, r, c][14 6 10; 4] *
+            env.corners[SOUTHWEST, r, c][4; 2] *
+            env.edges[WEST, r, c][2 7 9; 1] *
+            peps[r, c][29; 5 15 6 7] *
+            conj(peps[r, c][29; 8 19 10 9]) *
+            peps[r, cnext][30; 16 25 17 15] *
+            conj(peps[r, cnext][30; 22 26 21 19])
+        end
         o / n
     end
 end