Add Neighborhood Tensor Update (NTU) #144
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| #= | ||
| 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 | ||
| =# | ||
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| """ | ||
| Algorithms to construct bond environment for Neighborhood Tensor Update (NTU). | ||
| """ | ||
| abstract type NeighbourEnv end | ||
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| """ | ||
| SVD which truncion only keeping the leading singular value in the trivial sector. | ||
| """ | ||
| function _svd_cut!(t::AbstractTensorMap) | ||
| A, B = left_orth!(t; trunc = truncspace(oneunit(spacetype(t)))) | ||
| return removeunit(A, numind(A)), removeunit(B, 1) | ||
| end | ||
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| """ | ||
| 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, Y, state::InfiniteState, alg::NNEnv | ||
| ) | ||
| 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 | ||
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Member
There was a problem hiding this comment. Do you need these to be normalized separately? In principle, by putting the entire |
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| @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 | ||
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| """ | ||
| 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, Y, state::InfiniteState, alg::NNpEnv | ||
| ) | ||
| 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) | ||
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| # ---- hairs (size D^2) with a 1D auxiliary leg ---- | ||
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| @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) | ||
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| @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) | ||
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| nw = permute(cor_nw(ms[-1, -1]), ((3, 4), (1, 2))) | ||
| nw1, nw2 = _svd_cut!(nw) | ||
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| ne = permute(cor_ne(ms[-1, 2]), ((3, 4), (1, 2))) | ||
| ne1, ne2 = _svd_cut!(ne) | ||
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| sw = permute(cor_sw(ms[1, -1]), ((1, 2), (3, 4))) | ||
| sw1, sw2 = _svd_cut!(sw) | ||
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| se = permute(cor_se(ms[1, 2]), ((3, 4), (1, 2))) | ||
| se1, se2 = _svd_cut!(se) | ||
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| m = ms[0, -1] | ||
| @tensoropt hW[DXw1 DXw0] := | ||
| hair_w(ms[0, -2])[Dw21 Dw20] * | ||
| nw1[Dnw11 Dnw10] * sw1[Dsw11 Dsw10] * | ||
| twistdual(m, 1)[p Dnw10 DXw0 Dsw10 Dw20] * | ||
| conj(m[p Dnw11 DXw1 Dsw11 Dw21]) | ||
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| m = ms[0, 2] | ||
| @tensoropt hE[DYe1 DYe0] := | ||
| hair_e(ms[0, 3])[De21 De20] * | ||
| ne2[Dne21 Dne20] * se2[Dse21 Dse20] * | ||
| twistdual(m, 1)[p Dne20 De20 Dse20 DYe0] * | ||
| conj(m[p Dne21 De21 Dse21 DYe1]) | ||
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| # ---- corners (size D^4) with a 1D auxiliary leg ---- | ||
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| m = ms[-1, 0] | ||
| @tensoropt NW[Dn1 Dn0 DXn1 DXn0] := | ||
| tl[Dtl1 Dtl0] * nw2[Dnw21 Dnw20] * | ||
| twistdual(m, 1)[p Dtl0 Dn0 DXn0 Dnw20] * | ||
| conj(m[p Dtl1 Dn1 DXn1 Dnw21]) | ||
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| m = ms[-1, 1] | ||
| @tensoropt NE[Dn1 Dn0 DYn1 DYn0] := | ||
| tr[Dtr1 Dtr0] * ne1[Dne11 Dne10] * | ||
| twistdual(m, 1)[p Dtr0 Dne10 DYn0 Dn0] * | ||
| conj(m[p Dtr1 Dne11 DYn1 Dn1]) | ||
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| m = ms[1, 0] | ||
| @tensoropt SW[DXs1 DXs0 Ds1 Ds0] := | ||
| bl[Dbl1 Dbl0] * sw2[Dsw21 Dsw20] * | ||
| twistdual(m, 1)[p DXs0 Ds0 Dbl0 Dsw20] * | ||
| conj(m[p DXs1 Ds1 Dbl1 Dsw21]) | ||
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| m = ms[1, 1] | ||
| @tensoropt SE[DYs1 DYs0 Ds1 Ds0] := | ||
| br[Dbr1 Dbr0] * se1[Dse11 Dse10] * | ||
| twistdual(m, 1)[p DYs0 Dse10 Dbr0 Ds0] * | ||
| conj(m[p DYs1 Dse11 Dbr1 Ds1]) | ||
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| # ---- left half ---- | ||
| @tensoropt benvL[Dn1 Dn0 Dw1 Dw0 Ds1 Ds0] := | ||
| hW[DXw1 DXw0] * | ||
| NW[Dn1 Dn0 DXn1 DXn0] * | ||
| SW[DXs1 DXs0 Ds1 Ds0] * | ||
| twistdual(X, 1)[p DXn0 Dw0 DXs0 DXw0] * | ||
| conj(X[p DXn1 Dw1 DXs1 DXw1]) | ||
| normalize!(benvL, Inf) | ||
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| # ---- right half ---- | ||
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| @tensoropt benvR[Dn1 Dn0 De1 De0 Ds1 Ds0] := | ||
| hE[DYe1 DYe0] * | ||
| NE[Dn1 Dn0 DYn1 DYn0] * | ||
| SE[DYs1 DYs0 Ds1 Ds0] * | ||
| twistdual(Y, 1)[p DYn0 DYe0 DYs0 De0] * | ||
| conj(Y[p DYn1 DYe1 DYs1 De1]) | ||
| normalize!(benvR, Inf) | ||
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| # ---- the full NN+ environment ---- | ||
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| @tensor benv[Dw1, De1; Dw0, De0] := | ||
| benvL[Dn1 Dn0 Dw1 Dw0 Ds1 Ds0] * | ||
| benvR[Dn1 Dn0 De1 De0 Ds1 Ds0] | ||
| normalize!(benv, Inf) | ||
| return benv | ||
| end | ||
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| """ | ||
| 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, Y, state::InfiniteState, alg::NNNEnv | ||
| ) | ||
| 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===●======● | ||
| 1 2 | ||
| =# | ||
| 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] | ||
|
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| normalize!(benv, Inf) | ||
| return benv | ||
| end | ||
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Out of curiosity: do you need the weight to be distributed equally? Otherwise this might be replaced with
left_orth!(t; trunc = truncrank(1))orright_orth!(t; trunc = truncrank(1)), which I think removes some intermediate allocations.There was a problem hiding this comment.
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On a separate note, do we need this to be trivially charged for everything to work? It might reduce quite a bit of the number of legs if we can do something like:
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Nice observation! Actually no, since this D = 1 leg is in the end contracted, so how we distribute
sis irrelevant.It seems that
_svd_cutis always applied to a positive map, which then (if my feeling is right) ensures that the leading singular value has trivial charge. I'll double-check this.In YASTN they don't need to worry about it, since they only support Abelian symmetries and allow a tensor to have nonzero total charge.