### iDMRG Convergence Issues

Posted:

**06 Oct 2023, 23:53**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.

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.