Extended Gutzwiller wave function for the Hubbard-Holstein model

¹  International School for Advanced Studies (SISSA) - Via Beirut 2-4, I-34014 Trieste, Italy
²  Dipartimento di Fisica “E. Amaldi," Università di Roma Tre - Via della Vasca Navale 84, 00146 Roma, Italy
³  Istituto dei Sistemi Complessi, CNR - Via dei Taurini 19, 00185 Roma, Italy
⁴  SMC, CNR-INFM and Dipartimento di Fisica, Università “La Sapienza" - P.le Aldo Moro 2, 00185 Roma, Italy
⁵  The Abdus Salam International Center for Theoretical Physics (ICTP) - P.O. Box 586, I-34014 Trieste, Italy

Received: 7 June 2007
Accepted: 28 June 2007

Abstract

We introduce a new type of Gutzwiller variational wave function for correlated electrons coupled to phonons, able to treat on equal footing electronic and lattice degrees of freedom. We benchmark the wave function in the infinite-U Hubbard-Holstein model away from half-filling on a Bethe lattice, where we can directly compare with exact results by the Dynamical Mean-Field Theory. For this model, we find that variational results agree perfectly well with the exact ones. In particular the wave function correctly describes the crossover to a heavy polaron gas upon increasing the electron-phonon coupling.