# Problem about convergence of tJ model

I calculate a simple tJ model ,however the energy is not convergent. The program and the result are below:#include "itensor/all.h"
using namespace itensor;

int main()
{
int L = 80;
double t = 1.0;
double Jz = 1.0;
auto sites = tJ(L);

auto ampo = AutoMPO(sites);
for(int j = 1; j < L; ++j)
{
ampo += -t,"Cdagup",j,"Cup",j+1;
ampo += -t,"Cdagup",j+1,"Cup",j;
ampo += -t,"Cdagdn",j,"Cdn",j+1;
ampo += -t,"Cdagdn",j+1,"Cdn",j;
ampo += Jz,"Sz",j,"Sz",j+1;
}
auto H = toMPO(ampo);

auto state = InitState(sites);
for(int j = 1; j <= L; ++j)
{
if(j%4==1)  state.set(j,"Up");
else if(j%4==2)  state.set(j,"Dn");
}
auto psi0 = MPS(state);
auto sweeps = Sweeps(20);
sweeps.noise() = 1E-6,1E-6,1E-8,1E-10,1E-12;
sweeps.maxdim() = 20,50,100,200;
sweeps.cutoff() = 1E-14;
auto [energy,psi] = dmrg(H,psi0,sweeps,"Quiet");

return 0;


}

Result:

vN Entropy at center bond b=40 = 4.331806189036
Eigs at center bond b=40: 0.0870 0.0848 0.0782 0.0761 0.0156 0.0150 0.0149 0.0142 0.0133 0.0128
Largest link dim during sweep 16/20 was 200
Largest truncation error: 5.56915e-06
Energy after sweep 16/20 is -50.801917299231
Sweep 16/20 CPU time = 27.42s (Wall time = 28.95s)

vN Entropy at center bond b=40 = 4.353591702822
Eigs at center bond b=40: 0.0883 0.0861 0.0764 0.0756 0.0149 0.0145 0.0144 0.0137 0.0126 0.0125
Largest link dim during sweep 17/20 was 200
Largest truncation error: 6.09279e-06
Energy after sweep 17/20 is -50.509784548999
Sweep 17/20 CPU time = 27.53s (Wall time = 28.85s)

vN Entropy at center bond b=40 = 4.370626565212
Eigs at center bond b=40: 0.0897 0.0870 0.0769 0.0731 0.0145 0.0145 0.0140 0.0131 0.0122 0.0119
Largest link dim during sweep 18/20 was 200
Largest truncation error: 6.65186e-06
Energy after sweep 18/20 is -50.664949183470
Sweep 18/20 CPU time = 27.84s (Wall time = 28.78s)

vN Entropy at center bond b=40 = 4.384005562025
Eigs at center bond b=40: 0.0920 0.0877 0.0747 0.0729 0.0144 0.0141 0.0136 0.0124 0.0115 0.0114
Largest link dim during sweep 19/20 was 200
Largest truncation error: 7.03868e-06
Energy after sweep 19/20 is -50.695774689683
Sweep 19/20 CPU time = 27.52s (Wall time = 28.37s)

vN Entropy at center bond b=40 = 4.393822650435
Eigs at center bond b=40: 0.0938 0.0887 0.0752 0.0701 0.0143 0.0137 0.0130 0.0117 0.0111 0.0108
Largest link dim during sweep 20/20 was 200
Largest truncation error: 7.32056e-06
Energy after sweep 20/20 is -50.292667154544
Sweep 20/20 CPU time = 27.61s (Wall time = 29.07s)


selected by

Hi, thanks for the question. Are you using the very latest version of ITensor on the v3 branch? We recently fixed a bug specifically with the tJ site set which was causing Hamiltonians made from it to not be Hermitian, which could lead to the behavior you are seeing.

Please pull and recompile ITensor and then please let me know if the behavior persists. If it does we'll be happy to look deeper into it.

Best regards,
Miles

commented by (230 points)
I upgrate itensor and the result works well. Thanks
Best regards,
Weijie Huang
commented by (36.6k points)
Great! Very glad to hear it and thank you for posting the update.