Electron-Phonon Interactions in Flat Band Systems

TL;DR

This paper investigates how electron-phonon interactions induce charge density wave phases in flat band systems on the Lieb lattice, revealing long-range order and transition temperatures at specific fillings.

Contribution

It demonstrates the emergence of charge density wave phases driven by electron-phonon coupling on the Lieb lattice, focusing on fillings where previous studies emphasized electron-electron interactions.

Findings

Charge density wave phases at one-third and two-thirds fillings.

Long-range density correlations between doubly occupied sites.

Calculated transition temperatures as a function of electron-phonon coupling.

Abstract

Existing Quantum Monte Carlo studies have investigated the properties of fermions on a Lieb (CuO$_2$) lattice interacting with an on-site, or near-neighbor electron-electron coupling. Attention has focused on the interplay of such interactions with the macroscopic degeneracy of local zero energy modes, from which Bloch states can be formed to produce a flat band in which energy is independent of momentum. The resulting high density of states, in combination with the Stoner criterion, suggests that there should be pronounced instabilities to ordered phases. Indeed, a theorem by Lieb rigorously establishes the existence of ferrimagnetic order. Here we study the charge density wave phases induced by electron-phonon coupling on the Lieb lattice, as opposed to previous work on electron-electron interactions. Our key result is the demonstration of charge density wave (CDW) phases at one-third and two-thirds fillings, characterized by long-range density density correlations between doubly occupied sites on the minority or majority sublattice, and an accompanying gap. We also compute the transition temperature to the ordered phase as a function of the electron-phonon coupling.