Extended Gutzwiller wavefunction for the Hubbard-Holstein model

TL;DR

This paper introduces a new Gutzwiller variational wavefunction that effectively captures electron-phonon interactions in the Hubbard-Holstein model, showing excellent agreement with exact results and accurately describing polaron crossover.

Contribution

A novel Gutzwiller wavefunction that treats electronic and lattice degrees of freedom on equal footing for correlated electron-phonon systems.

Findings

Wavefunction matches exact DMFT results.

Successfully describes the heavy polaron crossover.

Applicable to the infinite-U Hubbard-Holstein model.

Abstract

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