-
Notifications
You must be signed in to change notification settings - Fork 0
/
MPO_A_PBC_Inf_opt.m
134 lines (134 loc) · 4.79 KB
/
MPO_A_PBC_Inf_opt.m
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
function [result,qAvar,resultm,a0,c] = MPO_A_PBC_Inf_opt
figureofmerit = 1; % 1 = 2Tr(r'L)-Tr(rLL), 2 = ||2*r'-rL-Lr||^2/||2*r'||^2
d = 2;
ti = 1;
noiserange = 2;
alfa = 1; gamma = 2; beta = 0.1;
lherm = 1; % 1 = yes, /else/ = no
phi = 10^-2;
imprecision = 10^(-5/2);
ratio = 10^(-5/2);
bdpsimax = 1;
bdlmax = 100;
%rng('default')
resultm = zeros([1,100]);
integral0 = 2*alfa*(gamma*ti+exp(-gamma*ti)-1)/gamma^2+beta*ti;
integral1 = 2*alfa*(cosh(gamma*ti)-1)*exp(-1*gamma*ti)/gamma^2;
integral2 = 2*alfa*(cosh(gamma*ti)-1)*exp(-2*gamma*ti)/gamma^2;
bdpsi = 1;
bdl = 1;
a0 = sqrt(2/(d+1))*sin((1:d)*pi/(d+1));
a0 = permute(a0,[1,3,2]);
c = triu(ones(d)-eye(d));
c = 1i*phi*exp(-integral0/2)*c/(1+2*exp(-integral0)*sinh(integral1));
c = c+c';
c = eye(d)+c;
c = reshape(c,[bdl,bdl,d,d]);
[resultm(bdl,bdpsi),a0,c] = MPO_A_PBC_Inf(figureofmerit,d,bdpsi,bdl,ti,noiserange,integral0,integral1,integral2,lherm,phi,imprecision,a0,c);
while 1
while 1
if bdpsi == bdpsimax
break
else
a0old = a0;
bdpsi = bdpsi+1;
a0 = zeros([bdpsi,bdpsi,d]);
for i = 1:d
if i <= ceil(d/2)
a0oldihalf = triu(rot90(a0old(:,:,i),-1));
a0(1:bdpsi-1,2:bdpsi,i) = a0oldihalf;
a0(:,:,i) = a0(:,:,i)+a0(:,:,i).';
a0(:,:,i) = a0(:,:,i)+diag([0;diag(a0(:,:,i),2);0]);
a0(:,:,i) = rot90(a0(:,:,i),1);
a0(1,bdpsi,i) = ratio*(1+1i)*abs(a0(1,bdpsi-1,i));
a0(bdpsi,1,i) = conj(a0(1,bdpsi,i));
if i == ceil(d/2) && mod(d,2) == 1
a0(:,:,i) = (a0(:,:,i)+a0(:,:,i).')/2;
end
else
a0(:,:,i) = a0(:,:,d+1-i).';
end
end
tensors = {conj(a0),a0};
legs = {[-1,-3,1],[-2,-4,1]};
tm = ncon(tensors,legs);
tm = reshape(tm,[bdpsi*bdpsi,bdpsi*bdpsi]);
a0norm = eigs(tm,1);
a0norm = abs(a0norm)^(1/2);
a0 = a0/a0norm;
[resultm(bdl,bdpsi),a0new,cnew] = MPO_A_PBC_Inf(figureofmerit,d,bdpsi,bdl,ti,noiserange,integral0,integral1,integral2,lherm,phi,imprecision,a0,c);
if resultm(bdl,bdpsi) < (1+imprecision)*resultm(bdl,bdpsi-1)
bdpsi = bdpsi-1;
a0 = a0old;
a0copy = a0new;
ccopy = cnew;
break
else
a0 = a0new;
c = cnew;
end
end
end
if bdl == bdlmax
if bdpsi == bdpsimax
resultm = resultm(1:bdl,1:bdpsi);
result = resultm(bdl,bdpsi);
else
a0 = a0copy;
c = ccopy;
resultm = resultm(1:bdl,1:bdpsi+1);
result = resultm(bdl,bdpsi+1);
end
break
else
cold = c;
bdl = bdl+1;
factor = 1/2;
while 1
c = zeros([bdl,bdl,d,d]);
for nx = 1:d
for nxp = 1:d
if nx ~= nxp
meanrecold = sum(sum(abs(real(cold(:,:,nx,nxp)))))/(bdl-1)^2;
meanimcold = sum(sum(abs(imag(cold(:,:,nx,nxp)))))/(bdl-1)^2;
c(:,:,nx,nxp) = (meanrecold*rand(bdl)+1i*meanimcold*rand(bdl))*factor;
end
end
end
c = (c+conj(permute(c,[1,2,4,3])))/2;
c(1:bdl-1,1:bdl-1,:,:,:) = cold;
tensors = {c};
legs = {[-1,-2,1,1]};
tm = ncon(tensors,legs);
ctr = eigs(tm,1);
ctr = real(ctr);
c = d*c/ctr;
[resultm(bdl,bdpsi),a0new,cnew] = MPO_A_PBC_Inf(figureofmerit,d,bdpsi,bdl,ti,noiserange,integral0,integral1,integral2,lherm,phi,imprecision,a0,c);
if resultm(bdl,bdpsi) > resultm(bdl-1,bdpsi)
a0 = a0new;
c = cnew;
break
end
factor = factor/2;
end
if resultm(bdl,bdpsi) < (1+imprecision)*resultm(bdl-1,bdpsi)
if bdpsi == bdpsimax
resultm = resultm(1:bdl,1:bdpsi);
result = resultm(bdl,bdpsi);
else
if resultm(bdl,bdpsi) < resultm(bdl-1,bdpsi+1)
a0 = a0copy;
c = ccopy;
resultm = resultm(1:bdl,1:bdpsi+1);
result = resultm(bdl-1,bdpsi+1);
else
resultm = resultm(1:bdl,1:bdpsi+1);
result = resultm(bdl,bdpsi);
end
end
break
end
end
end
qAvar = (2*alfa+gamma*beta)/gamma-result;
end