Spreading of correlations in the Falicov-Kimball model

TL;DR

This paper investigates how charge correlations spread in the Falicov-Kimball model using lattice Monte Carlo simulations, revealing how interaction strength and temperature influence the velocity and range of correlation spreading.

Contribution

It provides the first detailed analysis of correlation spreading in the Falicov-Kimball model, including effects of temperature, interaction strength, and disorder, and benchmarks approximation methods against exact simulations.

Findings

Light-cone velocity decreases with interaction at low temperature.

Phase velocity increases with interaction.

Correlation range decreases with increasing interaction at high temperature.

Abstract

We study dynamical properties of the one- and two-dimensional Falicov-Kimball model using lattice Monte Carlo simulations. In particular, we calculate the spreading of charge correlations in the equilibrium model and after an interaction quench. The results show a reduction of the light-cone velocity with interaction strength at low temperature, while the phase velocity increases. At higher temperature, the initial spreading is determined by the Fermi velocity of the noninteracting system and the maximum range of the correlations decreases with increasing interaction strength. Charge order correlations in the disorder potential enhance the range of the correlations. We also use the numerically exact lattice Monte Carlo results to benchmark the accuracy of equilibrium and nonequilibrium dynamical cluster approximation calculations. It is shown that the bias introduced by the mapping to a periodized cluster is substantial, and that from a numerical point of view, it is more efficient to simulate the lattice model directly.