PEPSKit.jl/src/algorithms/contractions/transfer.jl at ace0e16e34f27fc9954c65225dd052d413773427 · QuantumKitHub/PEPSKit.jl · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
#
# Transfer function for (CTMRG) edges
#

edge_transfer_left(v, ::Nothing, A, B) = edge_transfer_left(v, A, B)
edge_transfer_right(v, ::Nothing, A, B) = edge_transfer_right(v, A, B)

"""
    edge_transfer_left(v, Et, Eb)

Apply an edge transfer matrix to the left.

```
 ┌─Et─
-v │
 └─qƎ─
```
"""
@generated function edge_transfer_left(
        v::AbstractTensorMap{<:Any, S, 1, N₁},
        Etop::CTMRGEdgeTensor{<:Any, S, N₂},
        Ebot::CTMRGEdgeTensor{<:Any, S, N₂}
    ) where {S, N₁, N₂}
    t_out = tensorexpr(:v, -1, -(2:(N₁ + 1)))
    t_top = tensorexpr(:Etop, 2:(N₂ + 1), -(N₁ + 1))
    t_bot = tensorexpr(:Ebot, (-1, (3:(N₂ + 1))...), 1)
    t_in = tensorexpr(:v, 1, (-(2:N₁)..., 2))
    return macroexpand(
        @__MODULE__, :(return @tensor $t_out := $t_in * $t_top * $t_bot)
    )
end


"""
    edge_transfer_right(v, Et, Eb)

Apply an edge transfer matrix to the right.

```
─Et─┐
 │  v-
─qƎ─┘
```
"""
@generated function edge_transfer_right(
        v::AbstractTensorMap{<:Any, S, 1, N₁},
        Etop::CTMRGEdgeTensor{<:Any, S, N₂},
        Ebot::CTMRGEdgeTensor{<:Any, S, N₂}
    ) where {S, N₁, N₂}
    t_out = tensorexpr(:v, -1, -(2:(N₁ + 1)))
    t_top = tensorexpr(:Etop, (-1, (3:(N₂ + 1))...), 1)
    t_bot = tensorexpr(:Ebot, (2, (3:(N₂ + 1))...), -(N₁ + 1))
    t_in = tensorexpr(:v, 1, (-(2:N₁)..., 2))
    return macroexpand(
        @__MODULE__, :(return @tensor $t_out := $t_top * $t_bot * $t_in)
    )
end

"""
    edge_transfer_left(v, O, Et, Eb)

Apply an edge transfer matrix to the left.

```
 ┌──Et─
 │  │
 v──O──
 │  │
 └──qƎ─
```
"""
function edge_transfer_left(
        v::CTMRGEdgeTensor{<:Any, S, 3},
        O::PEPSSandwich,
        Etop::CTMRGEdgeTensor{<:Any, S, 3},
        Ebot::CTMRGEdgeTensor{<:Any, S, 3},
    ) where {S}
    @autoopt @tensor v´[χ_SE D_E_above D_E_below; χ_NE] :=
        v[χ_SW D_W_above D_W_below; χ_NW] *
        Etop[χ_NW D_N_above D_N_below; χ_NE] *
        Ebot[χ_SE D_S_above D_S_below; χ_SW] *
        ket(O)[d; D_N_above D_E_above D_S_above D_W_above] *
        conj(bra(O)[d; D_N_below D_E_below D_S_below D_W_below])

    return v´
end
function edge_transfer_left(
        v::CTMRGEdgeTensor{<:Any, S, 2},
        O::PFTensor,
        Etop::CTMRGEdgeTensor{<:Any, S, 2},
        Ebot::CTMRGEdgeTensor{<:Any, S, 2},
    ) where {S}
    @autoopt @tensor v´[χ_SE D_E; χ_NE] :=
        v[χ_SW D_W; χ_NW] *
        Etop[χ_NW D_N; χ_NE] *
        Ebot[χ_SE D_S; χ_SW] *
        O[D_W D_S; D_N D_E]

    return v´
end

"""
    transfer_right(v, Et, Eb)

Apply an edge transfer matrix to the right.

```
──Et─┐
  │  │
──O──v
  │  │
──qƎ─┘
```
"""
function edge_transfer_right(
        v::CTMRGEdgeTensor{<:Any, S, 3},
        O::PEPSSandwich,
        Etop::CTMRGEdgeTensor{<:Any, S, 3},
        Ebot::CTMRGEdgeTensor{<:Any, S, 3},
    ) where {S}
    @autoopt @tensor v′[χ_NW D_W_above D_W_below; χ_SW] :=
        v[χ_NE D_E_above D_E_below; χ_SE] *
        Etop[χ_NW D_N_above D_N_below; χ_NE] *
        Ebot[χ_SE D_S_above D_S_below; χ_SW] *
        ket(O)[d; D_N_above D_E_above D_S_above D_W_above] *
        conj(bra(O)[d; D_N_below D_E_below D_S_below D_W_below])

    return v′
end
function edge_transfer_right(
        v::CTMRGEdgeTensor{<:Any, S, 2},
        O::PFTensor,
        Etop::CTMRGEdgeTensor{<:Any, S, 2},
        Ebot::CTMRGEdgeTensor{<:Any, S, 2},
    ) where {S}
    return @autoopt @tensor v′[χ_NW D_W; χ_SW] :=
        v[χ_NE D_E; χ_SE] *
        Etop[χ_NW D_N; χ_NE] *
        Ebot[χ_SE D_S; χ_SW] *
        O[D_W D_S; D_N D_E]

    return v′
end

"""
    edge_transfer_left(v, O, Et, Eb)

Apply an edge transfer matrix to the left on an excited vector.

```
 ┌──Et─
 │  │
-v──O──
 │  │
 └──qƎ─
```
"""
function edge_transfer_left(
        v::CTMRGEdgeTensor{<:Any, S, 4}, O::PEPSSandwich,
        Etop::CTMRGEdgeTensor{<:Any, S, 3}, Ebot::CTMRGEdgeTensor{<:Any, S, 3},
    ) where {S}
    return @autoopt @tensor v′[χ_SE D_E_above d_string D_E_below; χ_NE] :=
        v[χ_SW D_W_above d_string D_W_below; χ_NW] *
        Etop[χ_NW D_N_above D_N_below; χ_NE] *
        Ebot[χ_SE D_S_above D_S_below; χ_SW] *
        ket(O)[d; D_N_above D_E_above D_S_above D_W_above] *
        conj(bra(O)[d; D_N_below D_E_below D_S_below D_W_below])
end
function edge_transfer_left(
        v::CTMRGEdgeTensor{<:Any, S, 3}, O::PFTensor,
        Etop::CTMRGEdgeTensor{<:Any, S, 2}, Ebot::CTMRGEdgeTensor{<:Any, S, 2},
    ) where {S}
    return @autoopt @tensor v′[χ_SE D_E d_string; χ_NE] :=
        v[χ_SW D_W d_string; χ_NW] *
        Etop[χ_NW D_N; χ_NE] *
        Ebot[χ_SE D_S; χ_SW] *
        O[D_W D_S; D_N D_E]
end