Phase competition in a one-dimensional three-orbital Hubbard-Holstein model

TL;DR

This study investigates how electron-electron and electron-phonon interactions compete in a one-dimensional three-orbital Hubbard-Holstein model, revealing complex phase transitions including orbital-selective Mott, charge-density-wave, and metallic phases.

Contribution

It provides the first detailed quantum Monte Carlo analysis of phase competition in a 1D three-orbital Hubbard-Holstein model, extending understanding beyond previous infinite-dimensional studies.

Findings

Orbital-selective Mott and charge-density-wave phases compete with an intermediate metallic phase.

Large e-e and e-ph couplings lead to insulating states with short-range orbital correlations.

Results align with prior dynamical mean field theory studies, indicating dimension-independent physics.

Abstract

We study the interplay between the electron-phonon (e-ph) and on-site electron-electron (e-e) interactions in a three-orbital Hubbard-Holstein model on an extended one-dimensional lattice using determinant quantum Monte Carlo. For weak e-e and e-ph interactions, we observe a competition between an orbital-selective Mott phase (OSMP) and a (multicomponent) charge-density-wave (CDW) insulating phase, with an intermediate metallic phase located between them. For large e-e and e-ph couplings, the OSMP and CDW phases persist, while the metallic phase develops short-range orbital correlations and becomes insulating when both the e-e and e-ph interactions are large but comparable. Many of our conclusions are in line with those drawn from a prior dynamical mean field theory study of the two-orbital Hubbard-Holstein model [Phys. Rev. B 95, 12112(R) (2017)] in infinite dimension, suggesting that the competition between the e-ph and e-e interactions in multiorbital Hubbard-Holstein models leads to rich physics, regardless of the dimension of the system.