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 approxi- mation.

Sign problem in the Bethe approximation / Ramezanpour, Abolfazl; Zecchina, Riccardo. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - STAMPA. - 86:(2012), p. 155147. [10.1103/PhysRevB.86.155147]

Sign problem in the Bethe approximation

RAMEZANPOUR, ABOLFAZL;ZECCHINA, RICCARDO
2012

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 approxi- mation.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2505876
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo