Competing interactions and symmetry breaking in the Hubbard-Holstein model

Max-Planck Institute for Solid State Research - Heisenbergstr.1, 70569 Stuttgart, Germany, EU

Corresponding author: j.bauer@fkf.mpg.de

Received: 22 December 2009
Accepted: 6 April 2010

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 ω₀, 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-λ 0, where λ characterizes the phonon-induced effective attraction. The transition is continuous for small couplings and large phonon frequencies ω₀ and becomes discontinuous for large couplings and small values of ω₀. We comment on the possible relevance of this work for Ba_1-xK_xBiO₃.