Sign problem in the Bethe approximation
Abstract
We propose a messagepassing 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 replicasymmetric 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 meanfield approxi mation.
 Publication:

Physical Review B
 Pub Date:
 October 2012
 DOI:
 10.1103/PhysRevB.86.155147
 arXiv:
 arXiv:1208.0188
 Bibcode:
 2012PhRvB..86o5147R
 Keywords:

 05.30.d;
 71.10.Fd;
 71.15.m;
 Quantum statistical mechanics;
 Lattice fermion models;
 Methods of electronic structure calculations;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 19 pages, 9 figures, one figure added