Monte Carlo Study of Localization on a One-Dimensional Lattice

We study the equilibrium properties of a single quantum particle interacting with a classical lattice gas. We develop a path-integral formalism in which the quantum particle is represented by a closed, variable-step random walk on the lattice. After demonstrating that a Metropolis algorithm correctly predicts the properties of a free particle, we extend it to investigate the behavior of the quantum particle interacting with the lattice gas. Evidence of weak localization is observed under conditions of quenched disorder, while self-trapping clearly occurs for the fully annealed system. Compared with continuous space systems, convergence of Monte Carlo simulations in this minimum model is orders of magnitude faster in cpu time. Therefore the system behavior can be investigated for a much larger domain of thermodynamic parameters (e.g., density and temperature) in a reasonable time.