DMRG Convergence and Overlap with True Ground State

[fqian5]

What is your issue?

Hi,

I understand that DMRG is designed to converge the energy to within a specified threshold. However, I'm wondering if there is any functionality in the package to ensure that the algorithm always converges to a good approximation of the true ground state, rather than a nearby excited state.

In some of my simulations, the algorithm seems to converge either to the true ground state or to one of the low-lying excited states that still meet the energy error threshold. I'm interested in making a plot of maximum bond dimension vs. overlap with the true ground state, to verify whether increasing the bond dimension consistently improves the overlap.

Are there recommended strategies to bias the DMRG toward the correct state in these ambiguous cases?

Thanks!

[jcmgray]

Hi @fqian5, I'm not aware of functionality that can guarantee reaching the groundstate of that kind, indeed I believe it might be a provably hard problem. However there are various heuristic techniques (note I am not an expert in this area, and other packages like pyblock are more much advanced with respect to DMRG than quimb):

1. choosing a smaller or zero tolerance to not halt the search
2. choosing the initial state carefully or sampling various different intitial states
3. expanding the bond dimension with sufficient noise at each sweep to avoid getting stuck
4. generating the smaller bond dim MPS from the largest one, i.e. you generate the MPS with the largest bond dimension first, then use that as the starting point for DMRG with a smaller bond dimension and so forth. This can help with the lower bond dimension states.

[fqian5]

Thank you! I will try around.