Holstein polaron in two and three dimensions by quantum Monte Carlo

Abstract

A recently developed quantum Monte Carlo approach to the Holstein model with one electron [PRB 69, 024301 (2004)] is extended to two and three dimensional lattices. A moderate sign problem occurs, which is found to diminish with increasing system size in all dimensions, and not to affect simulations significantly. We present an extensive study of the influence of temperature, system size, dimensionality and model parameters on the small-polaron cross over. Results are extrapolated to remove the error due to the Trotter discretization, which significantly improves the accuracy. Comparison with existing work and other quantum Monte Carlo methods is made. The method can be extended to the many-electron case.

14 pages, 11 figures

References in corpus (20)

• On the Fermi Liquid to Polaron Crossover II: Double Exchange and the Physics of "Colossal" Magnetoresistance
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Density matrix renormalization group study of the polaron problem in the Holstein model
• Dynamical mean-field theory of the small polaron
• Polarons and bipolarons in strongly interacting electron-phonon systems
• Ferromagnetism and electron-phonon coupling in the manganites
• Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron
• Polaron band formation in the Holstein model
• Dimensionality effects on the Holstein polaron
• Quantum Monte Carlo and variational approaches to the Holstein model
• Dynamical Properties of small Polarons
• Optical conductivity of the Frohlich polaron
• Spectral function of electron-phonon models by cluster perturbation theory
• The small polaron crossover: comparison between exact results and vertex correction approximation
• Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron
• A new variational approach for the Holstein Molecular Crystal Model
• Effects of dimensionality and anisotropy on the Holstein polaron
• Single hole dynamics in the t-J model on two- and three-leg ladders
• Isotope effect on the electron band structure of doped insulators
• Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions

Cited by in corpus (5)

• The Green's Function of the Holstein Polaron
• Photoemission spectra of many-polaron systems
• Single polaron properties of the breathing-mode Hamiltonian
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• Bipolaron formation in 1D-3D quantum dots: A lattice quantum Monte Carlo approach