First- and Second Order Phase Transitions in the Holstein-Hubbard Model

TL;DR

This paper explores the phase transitions in the Holstein-Hubbard model, identifying conditions for metal-insulator transitions driven by electron-electron and electron-phonon interactions, and characterizing their order and properties.

Contribution

It provides a comprehensive phase diagram using multiple numerical methods, revealing the nature and order of transitions in the Holstein-Hubbard model.

Findings

Transition to Mott insulator is second order when U dominates.

Transition to bipolaronic state is first order at larger U.

Quasiparticle weight and double-occupancy vary with U and g.

Abstract

We investigate metal-insulator transitions in the Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant the transition is to a Mott-insulator; when the electron-phonon interaction dominates, the transition is to a localised bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to the bipolaronic state, which is clearly first order for larger values of U. We also present results for the quasiparticle weight and the double-occupancy as function of U and g.