Intermediate phase of the one dimensional half-filled Hubbard-Holstein model

TL;DR

This study uses numerical methods to analyze the one-dimensional half-filled Hubbard-Holstein model, revealing an intermediate metallic phase with dominant superconducting correlations between Peierls and Mott insulator phases.

Contribution

It confirms the existence of an intermediate metallic phase and characterizes its properties, which was previously speculative, in the phase diagram of the model.

Findings

Intermediate metallic phase confirmed between Peierls and Mott phases.

Luttinger liquid exponent K_rho>1 indicates dominant superconducting correlations.

Phase diagram mapped as a function of U, phonon coupling, and frequency.

Abstract

We present a detailed numerical study of the Hubbard-Holstein model in one dimension at half filling, including full finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete, with the Holstein phonon coupling acting as an effective negative Hubbard onsite interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or U>0 Mott insulator phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We present results confirming the intermediate metallic phase, and show that the Luttinger liquid correlation exponent K_rho>1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of onsite Hubbard U, phonon coupling constant, and phonon frequency.