How to make DMRG independent of initial state?

DMRG and Numerical Methods
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Hi, I’m using the DMRG algorithm to calculate the ground state of Hubbard-Hofstadter model.

\hat{H}=-J \sum_{j, m}\left({e}^{{i} j \phi_{{AB}}/2} \hat{a}_{j, m+1}^{\dagger} \hat{a}_{j, m}+{e}^{-{i} j \phi_{{AB}}/2} \hat{a}_{j+1, m}^{\dagger} \hat{a}_{j, m}+\text { H.c. }\right)

But when I use different state as initial state, I get different ground state. I think the ground state of a Hamiltonian should be independent of initial state.
How to solve this problem?

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It’s unfortunate that DMRG results can sometimes depend on the initial state that you use, but it is just a fact about how DMRG works. It is a kind of variational method, so it can become ‘stuck’ in a local optimum just like with other kinds of variational methods.

The main way to get results which are not dependent too much on the initial state are:

  1. choose a different initial state which is closer to the ground state, meaning closer either in overlap or having more similar properties to the ground state
  2. use additional techniques within DMRG to help it to converge. A key one is the “noise term” which can greatly help with DMRG convergence

For more information we have written about this here:
https://itensor.github.io/ITensors.jl/stable/faq/DMRG.html#Preventing-DMRG-from-getting-stuck-in-a-local-minimum

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In this case, I add the “noise term”, and then the problem seems to be solved. Thanks!

1 Like
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Glad to hear it!