iDMRG Convergence Issues

[stephenjnaus]

I'm having issues with iDRMG convergence, and was hoping someone might have an idea of what the issue is.

I'm modeling the following 1D Rydberg Chain Hamiltonian:

H = \(\Sigma [ \Omega (b_j + b_j^+) + V_1 n_j n_{j+1} - \Delta n_j]\)

with the following representations for operators in the Pauli basis:

\(X_j = b_j + b_j^+\)
\(Z_j = 2n_j-1\)

In the blockade regime with \(V_1 = 100\), the system is critical at \(\Delta = 0.664, \Omega = 1.\)

I was able to run finite DMRG with PBC at this point and it converges with the state exhibiting expected power law scaling in its connected correlators. I was able to recover both the Z_2 phase and disordered phase in infinite DMRG, as well. However, when tuning the Hamiltonian to the critical point in infinite DMRG (unit cell size = 2), I experience convergence issues. The energy fluctuates significantly even after a large number of sweeps. I've tried turning the mixer on and off, different chi_lists/chi_max, increasing the number of sweeps, and a few other tests but to no avail.

I was thinking the issue might be the large value of \(V_1\) compared to the other parameters in my Hamiltonian, but I don't see why this issue wouldn't also arise when doing finite DMRG. Any thoughts on what may be the issue, here? Any insight would be much appreciated.

[DhruvT]

Maybe this is already quite late but are you able to obtain the ground state using iDMRG in canonical form? I expect that iDMRG cannot just converge at the critical point since it corresponds to a gapless state and thus cannot be expressed by an iMPS of finite dimension. I think that you are able to obtain results using DMRG because of finite size of the system whereas in iDMRG you are looking at the result in the thermodynamic limit where the ground state cannot be approximated by any finite bond dimension.