Hi,
I want to calculate <S^z(t)> as a function of ttotal for XXZ chain. Therefore I used both applyMPO and trotter gate and compared both results.
tstep=0.05 in both cases.
I just replaced
auto nt = int(ttotal/tau+(1e-9*(ttotal/tau)));
for(int n = 1; n <= nt; ++n)
{
psiz1 = applyMPO(expH1,psiz1,args);
psiz1.noPrime().normalize();
}
with
gateTEvol(gates,ttotal,tstep,psiz1,{“Cutoff=”,cutoff,“Verbose=”,true});
Using trotter gate: for t>0 <S^z(t)> is not changing.
ttotal <Sz_i(t)> real(<Sz_i(t)>)
0 (-0.475,0) -0.475
0.05 (-0.475,9.06017e-05) -0.475
0.1 (-0.474999,0.00018107) -0.474999
0.15 (-0.474997,0.000271279) -0.474997
0.2 (-0.474996,0.00036112) -0.474996
0.25 (-0.474993,0.000450503) -0.474993
0.3 (-0.474991,0.000539368) -0.474991
0.35 (-0.474988,0.000627684) -0.474988
0.4 (-0.474986,0.00071545) -0.474986
0.45 (-0.474983,0.000802697) -0.474983
0.5 (-0.474981,0.000889483) -0.474981
0.55 (-0.474979,0.000975886) -0.474979
0.6 (-0.474978,0.00106201) -0.474978
0.65 (-0.474977,0.00114795) -0.474977
0.7 (-0.474976,0.00123383) -0.474976
0.75 (-0.474976,0.00131975) -0.474976
0.8 (-0.474976,0.00140581) -0.474976
0.85 (-0.474977,0.00149209) -0.474977
0.9 (-0.474977,0.00157865) -0.474977
0.95 (-0.474978,0.00166554) -0.474978
1 (-0.474979,0.00175277) -0.474979
Using applyMPO:for t>0 <S^z(t)> is oscillating
ttotal <Sz_i(t)> real(<Sz_i(t)>)
0 (0.45125,0) 0.45125
0.05 (0.451157,-0.0175017) 0.451157
0.1 (0.450327,-0.0350436) 0.450327
0.15 (0.44876,-0.0525982) 0.44876
0.2 (0.446454,-0.0701363) 0.446454
0.25 (0.443414,-0.0876265) 0.443414
0.3 (0.439646,-0.105036) 0.439646
0.35 (0.435156,-0.122329) 0.435156
0.4 (0.429957,-0.139472) 0.429957
0.45 (0.424059,-0.156429) 0.424059
0.5 (0.417475,-0.173163) 0.417475
0.55 (0.410222,-0.189638) 0.410222
0.6 (0.402314,-0.205821) 0.402314
0.65 (0.39377,-0.221678) 0.39377
0.7 (0.384606,-0.237175) 0.384606
0.75 (0.374842,-0.252283) 0.374842
0.8 (0.364497,-0.266972) 0.364497
0.85 (0.353591,-0.281215) 0.353591
0.9 (0.342144,-0.294988) 0.342144
0.95 (0.330178,-0.308267) 0.330178
1 (0.317713,-0.321031) 0.317713