Competing interactions and symmetry breaking in the Hubbard-Holstein model

TL;DR

This paper investigates the competition between Coulomb repulsion and electron-phonon interactions in the Hubbard-Holstein model, revealing phase transitions between antiferromagnetic and charge-ordered states depending on interaction strengths and phonon frequency.

Contribution

It provides a detailed phase diagram of the Hubbard-Holstein model in large dimensions, highlighting the nature of quantum phase transitions influenced by interaction parameters.

Findings

Quantum phase transition from AFM to CO occurs near U - λ ≈ 0.

Transition is continuous at high phonon frequencies and small couplings.

Transition becomes discontinuous at low phonon frequencies and large couplings.

Abstract

Competing interactions are often responsible for intriguing phase diagrams in correlated electron systems. Here we analyze the competition of instantaneous short range Coulomb interaction $U$ with the retarded electron-electron interaction induced by an electron-phonon coupling $g$ as described by the Hubbard-Holstein model. The ground state phase diagram of this model in the limit of large dimensions at half filling is established. The study is based on dynamical mean field theory combined with the numerical renormalization group. Depending on $U$, $g$, and the phonon frequency $\omega_0$, the ground state is antiferromagnetically (AFM) or charge ordered (CO). We find quantum phase transitions from the AFM to CO state to occur when $U-\lambda\simeq 0$, where $\lambda$ characterizes the phonon induced effective attraction. The transition is continuous for small couplings and large phonon frequencies $\omega_0$ and becomes discontinuous for large couplings and small values of $\omega_0$. We comment on the possible relevance of this work for Ba${}_{1-x}$K${}_x$BiO${}_3$.