# expectation value of expH

+1 vote

When I am running this code for psi0 being the ground state of 64-site heisenberg model,

auto tau = 0.0001;
auto expH = toExpH(ampo,tau*Cplx_i);
printfln("%.16c", innerC(psi0, expH, psi0));


I'm expecting the imaginary part of the answer to be around the value of tau*E0, which is estimated by the taylor expansion. However it's half the value.

(0.9999990471106844,0.001408770830011393)


ground state:

vN Entropy at center bond b=32 = 0.845274370251
Eigs at center bond b=32: 0.7615 0.0773 0.0773 0.0773 0.0018 0.0018 0.0018
Largest link dim during sweep 100/100 was 82
Largest truncation error: 8.2362e-11
Energy after sweep 100/100 is -28.175424840952
Sweep 100/100 CPU time = 0.433s (Wall time = 0.478s)

Ground State Energy = -28.1754248410


I don't know what's the wrong in this difference between my expectation and result.

commented by (14.1k points)
The approximation is not just a simple Taylor series, but a more complicated MPO construction as described here: https://tensornetwork.org/mps/algorithms/timeevo/mpo.html

So it may not be so simple to compute the exact error you expect. Miles is the expert on this so I'm sure he can say more about it.