Strong-coupling expansions for the anharmonic Holstein model and for the Holstein-Hubbard model

TL;DR

This paper develops a strong-coupling expansion for the anharmonic Holstein and Holstein-Hubbard models, revealing that anharmonicity significantly influences phase behavior and favors superconductivity over charge-density waves.

Contribution

It introduces a fourth-order strong-coupling expansion and mean-field analysis for these models, highlighting the impact of anharmonicity on phase diagrams.

Findings

Anharmonic effects are not replicable by Coulomb repulsion.

Anharmonicity enhances superconductivity.

Small anharmonicity significantly alters phase diagrams.

Abstract

A strong-coupling expansion is applied to the anharmonic Holstein model and to the Holstein-Hubbard model through fourth order in the hopping matrix element. Mean-field theory is then employed to determine transition temperatures of the effective (pseudospin) Hamiltonian. We find that anharmonic effects are not easily mimicked by an on-site Coulomb repulsion, and that anharmonicity strongly favors superconductivity relative to charge-density-wave order. Surprisingly, the phase diagram is strongly modified by relatively small values of the anharmonicity.