Gutzwiller scheme for electrons and phonons: the half-filled Hubbard-Holstein model

TL;DR

This paper introduces a generalized Gutzwiller wavefunction that includes phononic degrees of freedom to analyze the ground-state properties of the half-filled Hubbard-Holstein model, capturing complex electron-electron and electron-phonon interactions.

Contribution

It develops a flexible variational wavefunction that improves upon previous methods, enabling detailed study of phase transitions in strongly correlated electron-phonon systems.

Findings

Accurately describes Mott and bipolaronic transitions

Recovers previous variational approaches as special cases

Accesses previously inaccessible phase diagram regions

Abstract

We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by means of a generalized Gutzwiller wavefunction which includes phononic degrees of freedom. We study in detail the paramagnetic half-filled Hubbard-Holstein model, where the electron-electron interaction can lead to a Mott transition, and the electron-phonon coupling to a bipolaronic transition. We critically discuss the quality of the proposed wavefunction in describing the various transitions and crossovers that occur as a function of the parameters. Previous variational attempts are recovered as particular choices of the wavefunction, while keeping all the variational freedom allows to access regions of the phase diagram otherwise inaccessible within previous variational approaches.