Long-range charge order in the extended Holstein--Hubbard model

TL;DR

This paper rigorously proves the existence of long-range charge order in the extended Holstein--Hubbard model at low temperatures, highlighting phase competition between charge and antiferromagnetic orders in higher dimensions.

Contribution

It provides a rigorous proof of long-range charge order in the extended Holstein--Hubbard model under strong interactions at low temperatures.

Findings

Long-range charge order exists at low temperatures in three or more dimensions.

Phase competition between antiferromagnetic and charge orders is justified.

Strong electron-phonon and electron-electron interactions are key to charge order.

Abstract

This study investigated the extended Holstein--Hubbard model at half-filling as a model for describing interplay of the electron-electron and electron-phonon couplings. When the electron-phonon and nearest-neighbor electron-electron interactions are strong, we prove the existence of long-range charge order at sufficiently low temperature in three or more dimensions. As a result, we rigorously justify the phase competition between the antiferromagnetic and charge orders.