Entanglement entropy of ground state MPS from DMRG

[Sunny]

Hi,

I am trying to find the entanglement entropy at a critical point belonging to the Ising universality class.
I get the usual semi circular trend for the entanglement entropy for system sizes 64 and 128 as shown below
But for sizes 256 and 512 I get two peaks on the sides with a valley in the middle.
Could anyone tell why I am getting this discrepancy and how to fix it, if possible.
Is it perhaps because of the thrown out singular values during the truncations, or is it because I am not exactly at the critical point or some other reason altogether?

The DMRG converged well with an energy tolerance of 10e-8. Two point expectations are also coming as expected. I had set the singular values cutoff at 10e-11 and did roughly 30-40 sweeps until the energy converged starting from 50 bond dimensions and gradually going up to 400, though DMRG converged at roughly 200 bond dimensions only.
Thanks,
Jay.

[miles]

Are you using a Hamiltonian with periodic boundary conditions here? If so, no problem as that can be a good idea when computing central charge, but if so, I would say that 256 and 512 are going to be very challenging sizes to reach. You might actually need much larger bond dimensions and even worse, you could be getting “stuck” where the MPS is lacking correlations that go around the back of the circle (e.g. similar to the edge errors you are seeing) but where DMRG, which is doing open-boundary style MPS, can’t figure out how to put these correlations in, in a sense.

So mainly for this technque I would recommend carefully extrapolating from smaller system sizes only.