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

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.

arXiv commentFinal version

References in corpus (7)

• The Holstein Polaron
• On the Fermi Liquid to Polaron Crossover I: General Results
• Dynamical mean-field theory of the small polaron
• Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron
• The Charge Ordered State from Weak to Strong Coupling
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• Supersolid Phase Accompanied by a Quantum Critical Point in the Intermediate Coupling Regime of the Holstein Model
• Polaron and bipolaron tendencies in a semiclassical model for hole-doped bismuthates
• Thermal and quantum lattice fluctuations in Peierls chains