Energy calculation for degenerate states

DMRG and Numerical Methods
1

Hi ITensor group,

I have an question about calculating degenerate states. Suppose a system is doubly or triple or some degeneracy present at the ground state. So , for that how to calculate the states and their corresponding energies? Like in some literature to understand whether a phase is an Symmetry protected topological phase or not they have calculated this degenerate energy gap. For your reference please check PRL 128, 043402 (2022) paper.

Thanks,

2

The answer to this question depends on a couple of things:

  1. why is the degeneracy there? Is it a symmetry effect or something more fundamental like topological order? Is it a bulk or boundary effect?
  2. what information do you need to know? Are you interested in excited states? Why do you need all the ground states (e.g. for what purpose)? Etc.

Depending on the answers to these questions there are two things you can do. One is to remove the degeneracy if you understand its origin. For example modifying the boundary conditions or applying a small external field are two possible ways to remove degeneracies.

The other option is to calculate all of the ground states. For a finite DMRG calculation a good way to do this is to use our “excited state DMRG” which you can find an example of at this link.