Dynamical mean-field theory of Hubbard-Holstein model at half-filling: Zero temperature metal-insulator and insulator-insulator transitions

TL;DR

This paper uses dynamical mean-field theory and numerical renormalization group to map out the zero-temperature phase diagram of the Hubbard-Holstein model, revealing distinct metal and insulator phases driven by electron-electron and electron-phonon interactions.

Contribution

It provides a detailed phase diagram at zero temperature showing how U and g induce different transitions in the Hubbard-Holstein model, highlighting the non-adiabatic connection between insulating states.

Findings

Identifies metal, Mott-Hubbard insulator, and bipolaron insulator phases.

Shows phase transitions are driven by increasing U and g.

Demonstrates the insulating states are distinct and not connected adiabatically.

Abstract

We study the Hubbard-Holstein model, which includes both the electron-electron and electron-phonon interactions characterized by $U$ and $g$, respectively, employing the dynamical mean-field theory combined with Wilson's numerical renormalization group technique. A zero temperature phase diagram of metal-insulator and insulator-insulator transitions at half-filling is mapped out which exhibits the interplay between $U$ and $g$. As $U$ ($g$) is increased, a metal to Mott-Hubbard insulator (bipolaron insulator) transition occurs, and the two insulating states are distinct and can not be adiabatically connected. The nature of and transitions between the three states are discussed.