Phase diagram of the one dimensional Hubbard-Holstein Model at 1/2 and 1/4 filling

TL;DR

This paper maps the phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling, revealing the sequence of phases and the nature of phase transitions driven by electron-phonon and electron-electron interactions.

Contribution

It provides a detailed numerical analysis of phase transitions and the existence of an intermediate phase in the 1D Hubbard-Holstein model at different fillings.

Findings

An intermediate phase with a spin gap but no charge gap exists between Peierls and Mott states.

Transitions between phases are of the Kosterlitz-Thouless type, merging into a first-order transition at larger U.

An intermediate phase also appears at quarter filling.

Abstract

The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electron-phonon interactions. In one dimension at half filling the Holstein electron-phonon coupling promotes onsite pairs of electrons and a Peierls charge density wave while the Hubbard onsite Coulomb repulsion U promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that (i) As the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-U Hubbard model. (ii) The transitions between Mott/intermediate and intermediate/Peierls states are of the Kosterlitz-Thouless form. (iii) For larger U the two transitions merge at a tritical point into a single first order Mott/Peierls transition. In addition we show that an intermediate phase also occurs in the quarter-filled model.