Finding ground states of finite systems with fast vanishing gap
Posted: 06 Apr 2024, 19:41
Hello,
This is a general question about the validity of different algorithms for gapless systems and how to get reasonable results from tensor network methods for such systems.
I am trying to find the ground state of a system with a gap that closes at least as fast as \(O(1/N^2)\) for system size N. I am trying two-site DMRG at the moment, with a decaying subspace expansion mixer strength. I find that I receive the "FInal state not in canonical form warning" during many of my runs, which I am taking as a hint that DMRG is not converging for the given bond dimension. For a system size of L=8 with subspace expansion turned on, I find that a bond dimension of 256 is enough for convergence. Clearly, larger systems will need strong truncation of some kind. Do you have general advice on getting reasonable ground state approximations for such systems with fast vanishing gaps using Matrix product states? I considered using VUMPS, however, the Hamiltonian for the model I am considering has boundary projectors that enforce boundary conditions on edge spins - I am not entirely sure how this would translate to a uniform MPS Ansatz or if this even makes sense to do. Apologies if my question is too vague - in short, I am wondering if there are known strategies for dealing with gapless / vanishing gap systems with tensor networks for medium (~L=32/64) finite size systems.
Thank you!
This is a general question about the validity of different algorithms for gapless systems and how to get reasonable results from tensor network methods for such systems.
I am trying to find the ground state of a system with a gap that closes at least as fast as \(O(1/N^2)\) for system size N. I am trying two-site DMRG at the moment, with a decaying subspace expansion mixer strength. I find that I receive the "FInal state not in canonical form warning" during many of my runs, which I am taking as a hint that DMRG is not converging for the given bond dimension. For a system size of L=8 with subspace expansion turned on, I find that a bond dimension of 256 is enough for convergence. Clearly, larger systems will need strong truncation of some kind. Do you have general advice on getting reasonable ground state approximations for such systems with fast vanishing gaps using Matrix product states? I considered using VUMPS, however, the Hamiltonian for the model I am considering has boundary projectors that enforce boundary conditions on edge spins - I am not entirely sure how this would translate to a uniform MPS Ansatz or if this even makes sense to do. Apologies if my question is too vague - in short, I am wondering if there are known strategies for dealing with gapless / vanishing gap systems with tensor networks for medium (~L=32/64) finite size systems.
Thank you!