Reorganize trotter and apply_gate code

Author: Yue-Zhengyuan

src/PEPSKit.jl

@@ -104,7 +104,10 @@ include("algorithms/truncation/truncationschemes.jl")
 include("algorithms/truncation/fullenv_truncation.jl")
 include("algorithms/truncation/bond_truncation.jl")
 
-include("algorithms/time_evolution/evoltools.jl")
+include("algorithms/time_evolution/trotter_gate.jl")
+include("algorithms/time_evolution/trotter_mpo.jl")
+include("algorithms/time_evolution/apply_gate.jl")
+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")

src/algorithms/time_evolution/apply_gate.jl

@@ -0,0 +1,131 @@
+"""
+$(SIGNATURES)
+
+Use QR decomposition on two tensors `A`, `B` connected by a bond to get the reduced tensors.
+When `A`, `B` are PEPSTensors,
+```
+        2                   1                                   1
+        |                   |                                   |
+    5 -A/B- 3   ====>   4 - X ← 2   1 ← a - 3   1 - b → 3   4 → Y - 2
+        | ↘                 |            ↘           ↘          |
+        4   1               3             2           2         3
+```
+When `A`, `B` are PEPOTensors, 
+- If `gate_ax = 1`
+```
+    2   3                1  2                                1  2
+      ↘ |                 ↘ |                                 ↘ |
+    6 -A/B- 4   ====>   5 - X ← 3   1 ← a - 3   1 - b → 3   5 → Y - 3
+        | ↘                 |            ↘           ↘          |
+        5   1               4             2           2         4
+```
+- If `gate_ax = 2`
+```
+    2   3                   2         2           2             2
+      ↘ |                   |          ↘           ↘            |
+    6 -A/B- 4   ====>   5 - X ← 3   1 ← a - 3   1 - b → 3   5 → Y - 3
+        | ↘                 | ↘                                 | ↘
+        5   1               4  1                                4  1
+```
+"""
+function _qr_bond(A::PT, B::PT; gate_ax::Int = 1) where {PT <: Union{PEPSTensor, PEPOTensor}}
+    @assert 1 <= gate_ax <= numout(A)
+    permA, permB, permX, permY = if A isa PEPSTensor
+        ((2, 4, 5), (1, 3)), ((2, 3, 4), (1, 5)), (1, 4, 2, 3), Tuple(1:4)
+    else
+        if gate_ax == 1
+            ((2, 3, 5, 6), (1, 4)), ((2, 3, 4, 5), (1, 6)), (1, 2, 5, 3, 4), Tuple(1:5)
+        else
+            ((1, 3, 5, 6), (2, 4)), ((1, 3, 4, 5), (2, 6)), (1, 2, 5, 3, 4), Tuple(1:5)
+        end
+    end
+    X, a = left_orth(permute(A, permA); positive = true)
+    Y, b = left_orth(permute(B, permB); positive = true)
+    # no longer needed after TensorKit 0.15
+    # @assert !isdual(space(a, 1))
+    # @assert !isdual(space(b, 1))
+    X, Y = permute(X, permX), permute(Y, permY)
+    b = permute(b, ((3, 2), (1,)))
+    return X, a, b, Y
+end
+
+"""
+$(SIGNATURES)
+
+Reconstruct the tensors connected by a bond from their `_qr_bond` results.
+For PEPSTensors,
+```
+        -2                             -2
+        |                               |
+    -5- X - 1 - a - -3     -5 - b - 1 - Y - -3
+        |        ↘               ↘      |
+        -4        -1              -1   -4
+```
+For PEPOTensors
+```
+    -2  -3                          -2  -3
+      ↘ |                             ↘ |
+    -6- X - 1 - a - -4     -6 - b - 1 - Y - -4
+        |        ↘               ↘      |
+        -5        -1              -1   -5
+
+        -3   -2              -2        -3
+        |      ↘               ↘        |
+    -6- X - 1 - a - -4     -6 - b - 1 - Y - -4
+        | ↘                             | ↘
+        -5 -1                          -5  -1
+```
+"""
+function _qr_bond_undo(X::PEPSOrth, a::AbstractTensorMap, b::AbstractTensorMap, Y::PEPSOrth)
+    @tensor A[-1; -2 -3 -4 -5] := X[-2 1 -4 -5] * a[1 -1 -3]
+    @tensor B[-1; -2 -3 -4 -5] := b[-5 -1 1] * Y[-2 -3 -4 1]
+    return A, B
+end
+function _qr_bond_undo(X::PEPOOrth, a::AbstractTensorMap, b::AbstractTensorMap, Y::PEPOOrth)
+    if !isdual(space(a, 2))
+        @tensor A[-1 -2; -3 -4 -5 -6] := X[-2 -3 1 -5 -6] * a[1 -1 -4]
+        @tensor B[-1 -2; -3 -4 -5 -6] := b[-6 -1 1] * Y[-2 -3 -4 -5 1]
+    else
+        @tensor A[-1 -2; -3 -4 -5 -6] := X[-1 -3 1 -5 -6] * a[1 -2 -4]
+        @tensor B[-1 -2; -3 -4 -5 -6] := b[-6 -2 1] * Y[-1 -3 -4 -5 1]
+    end
+    return A, B
+end
+
+"""
+$(SIGNATURES)
+
+Apply 2-site `gate` on the reduced matrices `a`, `b`
+```
+    -1← a --- 3 --- b ← -4          -2         -3
+        ↓           ↓               ↓           ↓
+        1           2               |----gate---|
+        ↓           ↓       or      ↓           ↓
+        |----gate---|               1           2
+        ↓           ↓               ↓           ↓
+        -2         -3           -1← a --- 3 --- b ← -4
+```
+"""
+function _apply_gate(
+        a::AbstractTensorMap, b::AbstractTensorMap,
+        gate::AbstractTensorMap{T, S, 2, 2}, trunc::TruncationStrategy
+    ) where {T <: Number, S <: ElementarySpace}
+    V = space(b, 1)
+    need_flip = isdual(V)
+    if isdual(space(a, 2))
+        @tensor a2b2[-1 -2; -3 -4] := gate[1 2; -2 -3] * a[-1 1 3] * b[3 2 -4]
+    else
+        @tensor a2b2[-1 -2; -3 -4] := gate[-2 -3; 1 2] * a[-1 1 3] * b[3 2 -4]
+    end
+    trunc = if trunc isa FixedSpaceTruncation
+        need_flip ? truncspace(flip(V)) : truncspace(V)
+    else
+        trunc
+    end
+    a, s, b, ϵ = svd_trunc!(a2b2; trunc, alg = LAPACK_QRIteration())
+    a, b = absorb_s(a, s, b)
+    if need_flip
+        a, s, b = flip(a, numind(a)), _fliptwist_s(s), flip(b, 1)
+    end
+    return a, s, b, ϵ
+end