Sign problem in the Bethe approximation

Abstract

We propose a message-passing algorithm to compute the Hamiltonian expectation with respect to an appropriate class of trial wave functions for an interacting system of fermions. To this end, we connect the quantum expectations to average quantities in a classical system with both local and global interactions, which are related to the variational parameters and use the Bethe approximation to estimate the average energy within the replica-symmetric approximation. The global interactions, which are needed to obtain a good estimation of the average fermion sign, make the average energy a nonlocal function of the variational parameters. We use some heuristic minimization algorithms to find approximate ground states of the Hubbard model on random regular graphs and observe significant qualitative improvements with respect to the mean-field approximation.

19 pages, 9 figures, one figure added

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• Statistical physics of loopy interactions: Independent-loop approximation and beyond
• Multilayer wave functions: A recursive coupling of local excitations
• Characterizing the parent Hamiltonian for a complete set of orthogonal wave functions: An inverse quantum problem