time evolution using trotter and applyMPO

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