Dear All, I am struggling with converging to the ground state of a BH model with unit filling with mps_optim with PBC. For low hopping it produces the same result as in the OBC case ignoring the boundary condition.
I have the following input <pasted below>. The state to which the mps_optim converges:
- has the same energy as the OBC hamiltonian for t<0.08 (the value of the constant varies it is larger for larger L) (see enclosed plot) and density artifacts at edges (similar to the OBC ground state)
- If I observe how the energy of a minimized state varies as a function of sweep number, then there are “plateaus” (for several iterations the energy seems to be converged, then it jumps down).. It seems that for small t the GS computation of mps_optim is stuck at the first plateau. So for say t<0.07 after each sweep starting from 5 the energy is constant but for larger t, at say sweep number 10 there is a sharp drop.
- none of the above happens for the OBC.
- I include file containing the difference between the numerical result and the essentially exact result (strong coupling expansion up to 16th order - actually I copied the formula only until 10th order). Clearly for all t between 0 and 0.06 the results are wrong, then they are fine again (and start to depart for larger t again but this is because I was to lazy to copy higher orders too)
- i have checked MAXSTATES=180 as well as MAXSTATES=320 (the results are exactly the same). For MAXSTATES=600 (and 120 sweeps and ietl_jcd_toll decreased to 1e-10) the results are almost the same again but now problems are for t<0.08 not for t<0.07 so in some sense situation is worse.
*************** questions ******************
I have thus two questions:
1. Is there a way to resolve it? 2. It seems that propagation of the PBC across the sample length (L=40 sites) gets truncated somehow. Still increasing number of states to 600 did not help. Is it what is going on or is it a bug?
Best, Mateusz Łącki
************* conf ****************** LATTICE="chain lattice" MODEL="boson Hubbard"
L=40
MAXSTATES=180
measure_each=5 init_state="local_quantumnumbers" initial_local_N='1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1' nsweeps=60
t=0.06; U=1.0; N_total=40 Nmax=5;
CONSERVED_QUANTUMNUMBERS='N' MEASURE[Entropy]=1 MEASURE_LOCAL[Local Density]='n'
{}
