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tdvp_1site_evolveKn.m
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function [mps, Vmat, para, results] = tdvp_1site_evolveKn(mps,Vmat,para,results,op,sitej,Cn,Hn)
%% Evolves the non-site center C(n) following Haegeman 2014
% - Only contains C = exp(i K(n) dt/2) C;
% - Varies for l->r and l<-r; uses para.sweepto
% - Hn input as (l*r*n,l*r*n) 2D-array
%
% Created by Florian Schroeder @ Cambridge 20/10/2014
t = para.tdvp.deltaT./2;
if para.tdvp.imagT
t = -1i*t;
end
if isempty(Hn) || numel(Cn) > para.tdvp.maxExpMDim && ~para.tdvp.expvCustomTestAccuracy
% Benchmarks show that expV is never better than expvCustom! So directly switch to it!
para.tdvp.expvCustomNow = 1; % in case, previous Hamiltonian became invalid (due to dimension changes), or expvCustom was used
end
writeResults = 0;
if nargout == 4 && ~isempty(results)
writeResults = 1;
end
evolveTreeCn = 0;
if sitej == 0 && para.useTreeMPS
% this is Cn between different tree levels. Either Node <-> Node or Node <-> leaf
evolveTreeCn = 1;
para.tdvp.expvCustomNow = 1;
% Only use Hleft/Hright from op
% return mps = Cn;
end
switch para.sweepto
case'r'
%% Get Dimensions
% A(n) = A_(l,r^,n), C(n) = C_(cl,cr); dim(r^) == dim(cl); dim(r)== dim(cr)
% Where: - A(n) - C(n) - A(n+1) -
% | |
% n n+1
[BondDimCLeft, BondDimCRight] = size(Cn); % BondDimCRight == true right bond dimension of non-site center
if para.tdvp.expvCustomNow == 0
%% prepare K(n) from H(n)
% through contraction with A(t+dt)
[BondDimALeft, BondDimARight, OBBDim] = size(mps{sitej}); % if no Vmat, then this = dk
assert(BondDimCLeft == BondDimARight);
if para.tdvp.expvCustomTestAccuracy
tempT = tic;
end
% K(n)_(rl',r',rl,r) = [A*_(l',rl',n') * H(n)_(l',r',n',l,r,n)]_(rl',r',l,r,n) * A_(l,rl,n)
Hn = reshape(Hn, [BondDimALeft, BondDimCRight, OBBDim, BondDimALeft, BondDimCRight, OBBDim]);
% Hn has dimensions like focused A(n)
Kn = contracttensors(conj(mps{sitej}),3,[1 3], Hn,6,[1 3]); % K(n)_(rl',r',l,r,n)
Kn = contracttensors(Kn,5,[3 5], mps{sitej},3,[1 3]); % K(n)_(rl',r',r,rl)
Kn = permute(Kn,[1,2,4,3]); % K(n)_(rl',r',rl,r)
Kn = reshape(Kn,[BondDimCLeft*BondDimCRight, BondDimCLeft*BondDimCRight]); % K(n)_(rl'r',rlr)
if para.tdvp.expvCustomTestAccuracy
results.tdvp.expvTime(end,16) = toc(tempT);
end
end
%% Take and apply Matrix exponential
% C(n,t) = exp(+ i K(n) dt)_(rl'*r',rl*r) * C(n,t+dt)_(rl*r)
if para.tdvp.expvCustomNow == 0 && size(Kn,1) <= para.tdvp.maxExpMDim
Cn = expm( 1i .* Kn .* t) * reshape(Cn,[numel(Cn),1]);
err = 0;
else
if para.tdvp.expvCustomNow
if evolveTreeCn
op.HleftAV = op.Hleft; % as calculated in H_Eff('TR-CA')
op.h2jAV = op.Opleft;
elseif ~isfield(op,'chain')
[op] = H_Eff(mps{sitej}, [] , 'CA', op, para); % standard chain H_Eff
else
op.HleftAV = op.chain(para.currentChain).Hleft; % from star-MPS into chain
op.h2jAV = op.chain(para.currentChain).Opleft;
% make sure H/Opright is correct
end
tempT = tic;
[Cn,err] = expvCustom(1i*t, 'Kn',Cn, para,op);
t15 = toc(tempT);
if para.tdvp.expvCustomTestAccuracy % debug
results.tdvp.expvTime(end,15) = t15;
end
else
if para.tdvp.expvCustomTestAccuracy % debug
tempT = tic;
Cn1 = expm( 1i .* Kn .* t) * reshape(Cn,[numel(Cn),1]); % Time expM
results.tdvp.expvTime(end,13) = toc(tempT);
tempT = tic;
[op] = H_Eff(mps{sitej}, [] , 'CA', op, para);
Cn1 = expvCustom(1i*t, 'Kn',Cn, para,op); % Time expvCustom
results.tdvp.expvTime(end,15) = toc(tempT);
tempT = tic;
end
[Cn,err] = expv(1i*t, Kn,...
reshape(Cn,[numel(Cn),1]),...
para.tdvp.expvTol, para.tdvp.expvM); % Time expV
if para.tdvp.expvCustomTestAccuracy
results.tdvp.expvTime(end,14) = toc(tempT);
end
if para.tdvp.expvCustomTestAccuracyRMS
disp(rms(Cn-Cn1)); % debug
end
end
end
if writeResults
% results.tdvp.expError(para.timeslice,para.expErrorI) = err; para.expErrorI = para.expErrorI+1;
results.tdvp.expError(para.timeslice,1) = max(results.tdvp.expError(para.timeslice,1),err);
end
Cn = reshape(Cn, [BondDimCLeft, BondDimCRight]);
clear('Kn', 'Hn');
%% Multiply Ac(n+1) = C(n) * Ar(n+1)
% set focus on next site A
% A_(rl,r,n) = C(n)_(rl,l) * A_(l,r,n)
if evolveTreeCn
nd = ndims(mps{sitej+1}); % sitej == 0
mps{sitej+1} = contracttensors(Cn,2,2, mps{sitej+1},nd,1); % possibility for node or leaf -> nd >= 3
else
mps{sitej+1} = contracttensors(Cn,2,2, mps{sitej+1},3,1);
end
clear('Cn');
case 'l'
%% Get Dimensions
% A(n+1) = A_(l^,r,n+1), C(n) = C_(cl,cr); dim(l^) == dim(cr)
% Where: - A(n) - C(n) - A(n+1) -
% | |
% n n+1
[BondDimCLeft, BondDimCRight] = size(Cn);
[BondDimALeft, BondDimARight, OBBDim] = size(mps{sitej+1}); % needed to reshape H(n+1)
assert(BondDimCRight == BondDimALeft);
if para.tdvp.expvCustomNow == 0
%% prepare K(n) from H(n+1)
% through contraction with A(t+dt)
% H(n) still persistent from previous sweep
% K(n)_(l',lr',l,lr) = [A*_(lr',r',n') * H(n+1)_(l',r',n',l,r,n)]_(lr',l',l,r,n) * A_(lr,r,n)
if para.tdvp.expvCustomTestAccuracy
tempT = tic;
end
Hn = reshape(Hn, [BondDimCLeft, BondDimARight, OBBDim, BondDimCLeft, BondDimARight, OBBDim]);
Kn = contracttensors(conj(mps{sitej+1}),3,[2 3], Hn,6,[2 3]); % K(n)_(lr',l',l,r,n)
Kn = contracttensors(Kn,5,[4 5], mps{sitej+1},3,[2 3]); % K(n)_(lr',l',l,lr)
Kn = permute(Kn,[2,1,3,4]); % K(n)_(l',lr',l,lr)
Kn = reshape(Kn,[BondDimCLeft*BondDimCRight, BondDimCLeft*BondDimCRight]); % K(n)_(l'*lr',l*lr)
if para.tdvp.expvCustomTestAccuracy
results.tdvp.expvTime(end,16) = toc(tempT);
end
end
%% Take and apply Matrix exponential
% C(n,t+dt/2) = exp(+ i K(n) dt/2)_(l'*lr',l*lr) * C(n,t+dt)_(l*lr)
if para.tdvp.expvCustomNow == 0
if size(Kn,1) <= para.tdvp.maxExpMDim
Cn = expm( 1i .* Kn .* para.tdvp.deltaT./2) *reshape(Cn,[numel(Cn),1]);
err = 0;
else
if para.tdvp.expvCustomTestAccuracy % debug
tempT = tic;
Cn1 = expm( 1i .* Kn .* para.tdvp.deltaT./2) *reshape(Cn,[numel(Cn),1]);
results.tdvp.expvTime(end,13) = toc(tempT);
tempT = tic;
[op] = H_Eff(mps{sitej+1}, [] , 'CA', op, para);
Cn1 = expvCustom(1i*t, 'Kn',Cn, para,op);
results.tdvp.expvTime(end,15) = toc(tempT);
tempT = tic;
end
[Cn,err] = expv(1i*t, Kn,...
reshape(Cn,[numel(Cn),1]),...
para.tdvp.expvTol, para.tdvp.expvM);
if para.tdvp.expvCustomTestAccuracy % debug
results.tdvp.expvTime(end,14) = toc(tempT);
end
if para.tdvp.expvCustomTestAccuracyRMS
disp(rms(Cn-Cn1)); % debug
end
end
else
if evolveTreeCn
op.HrightAV = op.Hright; % as calculated in H_Eff('TR-CA')
op.h2jAV = op.Opright;
else
[op] = H_Eff(mps{sitej+1}, [] , 'CA', op, para); % could be replaced if updateop called before
end
tempT = tic;
[Cn,err] = expvCustom(1i*t, 'Kn',Cn, para,op);
t15 = toc(tempT);
if para.tdvp.expvCustomTestAccuracy % debug
results.tdvp.expvTime(end,15) = t15;
end
end
if writeResults
% results.tdvp.expError(para.timeslice,para.expErrorI) = err; para.expErrorI = para.expErrorI+1;
results.tdvp.expError(para.timeslice,1) = max(results.tdvp.expError(para.timeslice,1),err);
end
Cn = reshape(Cn, [BondDimCLeft, BondDimCRight]);
clear('Kn', 'Hn');
if sitej == 0 || evolveTreeCn
mps = Cn; % shortcut for StarMPS
return;
end
%% Multiply Ac(n) = Al(n) * C(n)
% set focus on next site A
% A_(l,r,n) = A_(l,r',n) * C(n)_(r',r)
mps{sitej} = contracttensors(mps{sitej},3,2, Cn,2,1); % A_(l,n,r)
mps{sitej} = permute(mps{sitej},[1,3,2]); % A_(l,r,n)
clear('Cn');
end
end