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MPO_Fid_PBC_Inf.m
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MPO_Fid_PBC_Inf.m
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function result = MPO_Fid_PBC_Inf(a,b,phi)
% Parameters
figureofmerit = 1;
d = 2;
bdl = 1;
lherm = 1;
imprecision = 10^-(5/2);
tol1 = phi;
tol2 = phi;
d01 = 10^-1;
d02 = 10^-1;
h1 = 10^-10;
h2 = 10^-10;
relunc1 = 0.1*imprecision;
relunc2 = imprecision;
global ncon_skipCheckInputs;
ncon_skipCheckInputs = true;
% Functions
function y = pinv2(x,tol)
[uf,sf,vf] = svd(x);
sf = diag(sf);
positionf = sf > sf(1)*tol;
sf2 = sf(positionf).^-1;
sf2(end+1:numel(sf)) = 0;
sf2 = diag(sf2);
y = vf*sf2*uf';
end
function [fom1val,c,cnew] = fom1f(lambda,c,flag,cnew)
if lambda ~= 1
if flag ~= 1
tensorsf = {c,b};
legsf = {[-1,-3,1,2],[-2,-4,2,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhob,bdl*bdrhob]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l1r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhob]);
l1l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhob]);
tensorsf = {c,a,c};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdl,bdl*bdrhoa*bdl]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l2r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhoa,bdl]);
l2l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhoa,bdl]);
tensorsf = {l1l,b,l1r};
legsf = {[-1,2],[2,1,-4,-3],[-2,1]};
l1 = ncon(tensorsf,legsf);
l1 = reshape(l1,[bdl*bdl*d*d,1]);
tensorsf = {l2l,a,eye(d),l2r};
legsf = {[-1,2,-5],[2,1,-4,-7],[-8,-3],[-2,1,-6]};
l2 = ncon(tensorsf,legsf);
l2 = reshape(l2,[bdl*bdl*d*d,bdl*bdl*d*d]);
dl2 = l2+l2.';
dl1 = 2*l1;
dl2pinv = pinv2(dl2,tol1);
dl2pinv = (dl2pinv+dl2pinv.')/2;
cv = dl2pinv*dl1;
cnew = reshape(cv,[bdl,bdl,d,d]);
if lherm == 1
cnew = (cnew+conj(permute(cnew,[1,2,4,3])))/2;
end
tensorsf = {cnew};
legsf = {[-1,-2,1,1]};
tmf = ncon(tensorsf,legsf);
ctrf = eigs(tmf,1);
ctrf = real(ctrf);
cnew = d*cnew/ctrf;
if bdl == 1
cnew = reshape(cnew,[d,d]);
cnewmd = mean(diag(cnew));
cnew = imag(cnew);
cnew = (cnew+rot90(cnew,2).')/2;
cnew = cnewmd*eye(d)+1i*cnew;
cnew = reshape(cnew,[bdl,bdl,d,d]);
else
for nxf = 1:d
cnew(:,:,nxf,nxf) = zeros(bdl);
cnew(1,1,nxf,nxf) = 1;
end
end
end
c = (cnew*sin(lambda*pi)-c*cos(lambda*pi));
if lherm == 1
c = (c+conj(permute(c,[1,2,4,3])))/2;
end
tensorsf = {c};
legsf = {[-1,-2,1,1]};
tmf = ncon(tensorsf,legsf);
ctrf = eigs(tmf,1);
ctrf = real(ctrf);
c = d*c/ctrf;
if bdl == 1
c = reshape(c,[d,d]);
cmd = mean(diag(c));
c = imag(c);
c = (c+rot90(c,2).')/2;
c = cmd*eye(d)+1i*c;
c = reshape(c,[bdl,bdl,d,d]);
else
for nxf = 1:d
c(:,:,nxf,nxf) = zeros(bdl);
c(1,1,nxf,nxf) = 1;
end
end
end
tensorsf = {c,b};
legsf = {[-1,-3,1,2],[-2,-4,2,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhob,bdl*bdrhob]);
l1val = eigs(tmf,1);
tensorsf = {c,a,c};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdl,bdl*bdrhoa*bdl]);
l2val = eigs(tmf,1);
fom1val = real((2*l1val-l2val-1)/phi^2);
end
function [fom2val,c,cnew] = fom2f(lambda,c,flag,cnew)
if lherm == 1
if lambda ~= 1
if flag ~= 1
tensorsf = {c,b,a};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhob*bdrhoa,bdl*bdrhob*bdrhoa]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l1_1r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhob,bdrhoa]);
l1_1l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhob,bdrhoa]);
tensorsf = {c,a,b};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdrhob,bdl*bdrhoa*bdrhob]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l1_2r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhoa,bdrhob]);
l1_2l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhoa,bdrhob]);
tensorsf = {c,a,c,a};
legsf = {[-1,-5,1,2],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdl*bdrhoa,bdl*bdrhoa*bdl*bdrhoa]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l2_1r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhoa,bdl,bdrhoa]);
l2_1l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhoa,bdl,bdrhoa]);
tensorsf = {c,c,a,a};
legsf = {[-1,-5,1,2],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdl*bdrhoa*bdrhoa,bdl*bdl*bdrhoa*bdrhoa]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l2_2r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdl,bdrhoa,bdrhoa]);
l2_2l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdl,bdrhoa,bdrhoa]);
tensorsf = {l1_1l,b,a,l1_1r};
legsf = {[-1,4,5],[4,2,-4,1],[5,3,1,-3],[-2,2,3]};
l1_1 = ncon(tensorsf,legsf);
l1_1 = reshape(l1_1,[bdl*bdl*d*d,1]);
tensorsf = {l1_2l,a,b,l1_2r};
legsf = {[-1,4,5],[4,2,-4,1],[5,3,1,-3],[-2,2,3]};
l1_2 = ncon(tensorsf,legsf);
l1_2 = reshape(l1_2,[bdl*bdl*d*d,1]);
tensorsf = {l2_1l,a,a,l2_1r};
legsf = {[-1,2,-5,4],[2,1,-4,-7],[4,3,-8,-3],[-2,1,-6,3]};
l2_1 = ncon(tensorsf,legsf);
l2_1 = reshape(l2_1,[bdl*bdl*d*d,bdl*bdl*d*d]);
tensorsf = {l2_2l,eye(d),a,a,l2_2r};
legsf = {[-1,-5,4,5],[-4,-7],[4,2,-8,1],[5,3,1,-3],[-2,-6,2,3]};
l2_2 = ncon(tensorsf,legsf);
l2_2 = reshape(l2_2,[bdl*bdl*d*d,bdl*bdl*d*d]);
dl2 = l2_1+l2_1.'+l2_2+l2_2.';
dl1 = 2*(l1_1+l1_2);
dl2pinv = pinv2(dl2,tol2);
dl2pinv = (dl2pinv+dl2pinv.')/2;
cv = dl2pinv*dl1;
cnew = reshape(cv,[bdl,bdl,d,d]);
cnew = (cnew+conj(permute(cnew,[1,2,4,3])))/2;
tensorsf = {cnew};
legsf = {[-1,-2,1,1]};
tmf = ncon(tensorsf,legsf);
ctrf = eigs(tmf,1);
ctrf = real(ctrf);
cnew = d*cnew/ctrf;
if bdl == 1
cnew = reshape(cnew,[d,d]);
cnewmd = mean(diag(cnew));
cnew = imag(cnew);
cnew = (cnew+rot90(cnew,2).')/2;
cnew = cnewmd*eye(d)+1i*cnew;
cnew = reshape(cnew,[bdl,bdl,d,d]);
else
for nxf = 1:d
cnew(:,:,nxf,nxf) = zeros(bdl);
cnew(1,1,nxf,nxf) = 1;
end
end
end
c = (cnew*sin(lambda*pi)-c*cos(lambda*pi));
c = (c+conj(permute(c,[1,2,4,3])))/2;
tensorsf = {c};
legsf = {[-1,-2,1,1]};
tmf = ncon(tensorsf,legsf);
ctrf = eigs(tmf,1);
ctrf = real(ctrf);
c = d*c/ctrf;
if bdl == 1
c = reshape(c,[d,d]);
cmd = mean(diag(c));
c = imag(c);
c = (c+rot90(c,2).')/2;
c = cmd*eye(d)+1i*c;
c = reshape(c,[bdl,bdl,d,d]);
else
for nxf = 1:d
c(:,:,nxf,nxf) = zeros(bdl);
c(1,1,nxf,nxf) = 1;
end
end
end
tensorsf = {c,b,a};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhob*bdrhoa,bdl*bdrhob*bdrhoa]);
l1_1val = eigs(tmf,1);
tensorsf = {c,a,b};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdrhob,bdl*bdrhoa*bdrhob]);
l1_2val = eigs(tmf,1);
tensorsf = {c,a,c,a};
legsf = {[-1,-5,1,2],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdl*bdrhoa,bdl*bdrhoa*bdl*bdrhoa]);
l2_1val = eigs(tmf,1);
tensorsf = {c,c,a,a};
legsf = {[-1,-5,1,2],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdl*bdrhoa*bdrhoa,bdl*bdl*bdrhoa*bdrhoa]);
l2_2val = eigs(tmf,1);
fom2val = abs(1+(-4*(l1_1val+l1_2val)+2*(l2_1val+l2_2val))/(4*l0val));
else
if lambda ~= 1
if flag ~= 1
tensorsf = {conj(c),b,a};
legsf = {[-1,-4,2,1],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhob*bdrhoa,bdl*bdrhob*bdrhoa]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l1_1r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhob,bdrhoa]);
l1_1l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhob,bdrhoa]);
tensorsf = {conj(c),a,b};
legsf = {[-1,-4,2,1],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdrhob,bdl*bdrhoa*bdrhob]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l1_2r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhoa,bdrhob]);
l1_2l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhoa,bdrhob]);
tensorsf = {conj(c),a,c,a};
legsf = {[-1,-5,2,1],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdl*bdrhoa,bdl*bdrhoa*bdl*bdrhoa]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l2_1r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhoa,bdl,bdrhoa]);
l2_1l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhoa,bdl,bdrhoa]);
tensorsf = {conj(c),a,a,c};
legsf = {[-1,-5,2,1],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdrhoa*bdl,bdl*bdrhoa*bdrhoa*bdl]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l2_2r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdrhoa,bdrhoa,bdl]);
l2_2l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdrhoa,bdrhoa,bdl]);
tensorsf = {conj(c),c,a,a};
legsf = {[-1,-5,2,1],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdl*bdrhoa*bdrhoa,bdl*bdl*bdrhoa*bdrhoa]);
[tmvrf,~] = eigs(tmf,1);
[tmvlf,~] = eigs(tmf.',1);
tmvnorm = tmvlf.'*tmvrf;
l2_3r = reshape(tmvrf/tmvnorm^(1/2),[bdl,bdl,bdrhoa,bdrhoa]);
l2_3l = reshape(tmvlf.'/tmvnorm^(1/2),[bdl,bdl,bdrhoa,bdrhoa]);
tensorsf = {l1_1l,b,a,l1_1r};
legsf = {[-1,4,5],[4,2,-3,1],[5,3,1,-4],[-2,2,3]};
l1_1 = ncon(tensorsf,legsf);
l1_1 = reshape(l1_1,[bdl*bdl*d*d,1]);
tensorsf = {l1_2l,a,b,l1_2r};
legsf = {[-1,4,5],[4,2,-3,1],[5,3,1,-4],[-2,2,3]};
l1_2 = ncon(tensorsf,legsf);
l1_2 = reshape(l1_2,[bdl*bdl*d*d,1]);
tensorsf = {l2_1l,a,a,l2_1r};
legsf = {[-1,2,-5,4],[2,1,-3,-7],[4,3,-8,-4],[-2,1,-6,3]};
l2_1 = ncon(tensorsf,legsf);
l2_1 = reshape(l2_1,[bdl*bdl*d*d,bdl*bdl*d*d]);
tensorsf = {l2_2l,a,a,eye(d),l2_2r};
legsf = {[-1,4,5,-5],[4,2,-3,1],[5,3,1,-7],[-8,-4],[-2,2,3,-6]};
l2_2 = ncon(tensorsf,legsf);
l2_2 = reshape(l2_2,[bdl*bdl*d*d,bdl*bdl*d*d]);
tensorsf = {l2_3l,eye(d),a,a,l2_3r};
legsf = {[-1,-5,4,5],[-3,-7],[4,2,-8,1],[5,3,1,-4],[-2,-6,2,3]};
l2_3 = ncon(tensorsf,legsf);
l2_3 = reshape(l2_3,[bdl*bdl*d*d,bdl*bdl*d*d]);
dl2 = 2*l2_1+l2_2+l2_3;
dl2 = (dl2+dl2')/2;
dl1 = 2*(l1_1+l1_2);
dl2pinv = pinv2(dl2,tol2);
dl2pinv = (dl2pinv+dl2pinv')/2;
cv = dl2pinv*dl1;
cnew = reshape(cv,[bdl,bdl,d,d]);
tensorsf = {cnew};
legsf = {[-1,-2,1,1]};
tmf = ncon(tensorsf,legsf);
ctrf = eigs(tmf,1);
ctrf = real(ctrf);
cnew = d*cnew/ctrf;
if bdl == 1
cnew = reshape(cnew,[d,d]);
cnewmd = mean(diag(cnew));
cnew = imag(cnew);
cnew = (cnew+rot90(cnew,2).')/2;
cnew = cnewmd*eye(d)+1i*cnew;
cnew = reshape(cnew,[bdl,bdl,d,d]);
else
for nxf = 1:d
cnew(:,:,nxf,nxf) = zeros(bdl);
cnew(1,1,nxf,nxf) = 1;
end
end
end
c = (cnew*sin(lambda*pi)-c*cos(lambda*pi));
tensorsf = {c};
legsf = {[-1,-2,1,1]};
tmf = ncon(tensorsf,legsf);
ctrf = eigs(tmf,1);
ctrf = real(ctrf);
c = d*c/ctrf;
if bdl == 1
c = reshape(c,[d,d]);
cmd = mean(diag(c));
c = imag(c);
c = (c+rot90(c,2).')/2;
c = cmd*eye(d)+1i*c;
c = reshape(c,[bdl,bdl,d,d]);
else
for nxf = 1:d
c(:,:,nxf,nxf) = zeros(bdl);
c(1,1,nxf,nxf) = 1;
end
end
end
tensorsf = {conj(c),b,a};
legsf = {[-1,-4,2,1],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhob*bdrhoa,bdl*bdrhob*bdrhoa]);
l1_1val = eigs(tmf,1);
tensorsf = {conj(c),a,b};
legsf = {[-1,-4,2,1],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdrhob,bdl*bdrhoa*bdrhob]);
l1_2val = eigs(tmf,1);
tensorsf = {c,b,a};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhob*bdrhoa,bdl*bdrhob*bdrhoa]);
l1_3val = eigs(tmf,1);
tensorsf = {c,a,b};
legsf = {[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdrhob,bdl*bdrhoa*bdrhob]);
l1_4val = eigs(tmf,1);
tensorsf = {conj(c),a,c,a};
legsf = {[-1,-5,2,1],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdl*bdrhoa,bdl*bdrhoa*bdl*bdrhoa]);
l2_1val = eigs(tmf,1);
tensorsf = {conj(c),a,a,c};
legsf = {[-1,-5,2,1],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdrhoa*bdrhoa*bdl,bdl*bdrhoa*bdrhoa*bdl]);
l2_2val = eigs(tmf,1);
tensorsf = {conj(c),c,a,a};
legsf = {[-1,-5,2,1],[-2,-6,2,3],[-3,-7,3,4],[-4,-8,4,1]};
tmf = ncon(tensorsf,legsf);
tmf = reshape(tmf,[bdl*bdl*bdrhoa*bdrhoa,bdl*bdl*bdrhoa*bdrhoa]);
l2_3val = eigs(tmf,1);
fom2val = abs(1+(-2*(l1_1val+l1_2val+l1_3val+l1_4val)+2*l2_1val+l2_2val+l2_3val)/(4*l0val));
end
end
function [fom1,c] = fom1opt(c)
fom1 = zeros([100,1]);
fom1_1 = fom1f(1,c,0);
[fom1_05,c_05] = fom1f(1/2,c,0);
if fom1_05 > fom1_1
c = c_05;
fom1(1) = fom1_05;
else
fom1(1) = fom1_1;
end
fom1_1ph = fom1f(1+h1,c,0);
if fom1_1ph > fom1(1)
d1 = d01;
else
d1 = -d01;
end
testf = 0;
flag = 0;
cnew = [];
iter1 = 1;
while 1
iter1 = iter1+1;
[fom1val,c_1,c_2] = fom1f(1+d1,c,flag,cnew);
if fom1val > fom1(iter1-1)
c = c_1;
fom1(iter1) = fom1val;
testf = testf+1;
flag = 0;
else
d1 = d1/2;
fom1(iter1) = fom1(iter1-1);
testf = 0;
flag = 1;
cnew = c_2;
end
if abs(d1) < h1 || (testf >= 4 && all(fom1(iter1-3:iter1) > 0) && std(fom1(iter1-3:iter1),1)/mean(fom1(iter1-3:iter1)) <= relunc1)
break
end
end
fom1 = fom1(1:iter1);
%plot(fom1)
fom1 = fom1(iter1);
end
function [fom2,c] = fom2opt(c)
fom2 = zeros([100,1]);
fom2_1 = fom2f(1,c,0);
[fom2_05,c_05] = fom2f(1/2,c,0);
if fom2_05 < fom2_1
c = c_05;
fom2(1) = fom2_05;
else
fom2(1) = fom2_1;
end
fom2_1ph = fom2f(1+h2,c,0);
if fom2_1ph < fom2(1)
d2 = d02;
else
d2 = -d02;
end
testf = 0;
flag = 0;
cnew = [];
iter2 = 1;
while 1
iter2 = iter2+1;
[fom2val,c_1,c_2] = fom2f(1+d2,c,flag,cnew);
if fom2val < fom2(iter2-1)
c = c_1;
fom2(iter2) = fom2val;
testf = testf+1;
flag = 0;
else
d2 = d2/2;
fom2(iter2) = fom2(iter2-1);
testf = 0;
flag = 1;
cnew = c_2;
end
if abs(d2) < h2 || iter2 >= 40 || (testf >= 4 && std(fom2(iter2-3:iter2),1)/mean(fom2(iter2-3:iter2)) <= relunc2)
break
end
end
fom2 = fom2(1:iter2);
%plot(-log10(fom2))
fom2 = fom2(iter2);
end
% Calculations
% MPO
bdrhoa = size(a,1);
bdrhob = size(b,1);
c = triu(ones(d)-eye(d));
c = 1i*phi*exp(-1)*c;
c = c+c';
c = eye(d)+c;
c = reshape(c,[bdl,bdl,d,d]);
% [2Tr(rpL1)-Tr(rL1L1)-1]/phi^2 meanimization
if figureofmerit == 1
[fom1,~] = fom1opt(c);
f = fom1;
% ||2*rp-rL1-L1r2||^2/||2*rp||^2 minimization
elseif figureofmerit == 2
tensors = {a,a};
legs = {[-1,-3,1,2],[-2,-4,2,1]};
tm = ncon(tensors,legs);
tm = reshape(tm,[bdrhoa*bdrhoa,bdrhoa*bdrhoa]);
anorm = eigs(tm,1);
anorm = abs(anorm)^(1/2);
a = a/anorm;
b = b/anorm;
tensors = {b,b};
legs = {[-1,-3,1,2],[-2,-4,2,1]};
tm = ncon(tensors,legs);
tm = reshape(tm,[bdrhoa*bdrhoa,bdrhoa*bdrhoa]);
l0val = eigs(tm,1);
l0val = abs(l0val);
[fom2,c] = fom2opt(c);
a = a*anorm;
b = b*anorm;
f = fom1f(1,c);
end
result = f;
fids = 1/4*result;
fid = 1-1/8*result*phi^2;
end