The Many Electron Ground State of the Adiabatic Holstein Model in Two and Three Dimensions

TL;DR

This paper maps the complete ground state phase diagram of the classical phonon Holstein model in two and three dimensions, revealing various phases and the importance of spatial correlations.

Contribution

It introduces a new 'travelling cluster' approximation for large lattices and provides comprehensive phase diagrams considering phonon variables as classical.

Findings

Identification of Fermi liquid, polaron liquid, and charge ordered phases.

Phase coexistence region widens with increasing electron-phonon coupling.

Spatial correlations are crucial in understanding the strong coupling regime.

Abstract

We present the complete ground state phase diagram of the Holstein model in two and three dimension considering the phonon variables to be classical. We first establish the overall structure of the phase diagram by using exact diagonalisation based Monte Carlo (ED-MC) on small lattices and then use a new ``travelling cluster'' approximation (TCA) for annealing the phonon degrees of freedom on large lattices. The phases that emerge include a Fermi liquid (FL), with no lattice distortions, an insulating polaron liquid (PL) at strong coupling, and a charge ordered insulating (COI) phase around half- filling. The COI phase is separated from the Fermi liquid by a regime of phase coexistence whose width grows with increasing electron-phonon coupling. We provide results on the electronic density of states, the COI order parameter, and the spatial organisation of polaronic states, for arbitrary density and electron-phonon coupling. The results highlight the crucial role of spatial correlations in this strong coupling problem.