Path-integral approach to lattice polarons

Abstract

The basic principles behind a path integral approach to the lattice polaron are reviewed.Analytical integration of phonons reduces the problem to one self-interactingimaginary-time path, which is then simulated by Metropolis Monte Carlo. Projectionoperators separate states of different symmetry, which provides access to various excitedstates. Shifted boundary conditions in imaginary time enable calculation of the polaronmass, spectrum and density of states. Other polaron characteristics accessible by themethod include the polaron energy, number of excited phonons and isotope exponent onmass. Monte Carlo updates are formulated in continuous imaginary time on infinite latticesand as such provide statistically unbiased results without finite-size and finite time-steperrors. Numerical data are presented for models with short-range and long-rangeelectron–phonon interactions.