Nonequilibrium Dynamical Cluster Approximation study of the Falicov-Kimball Model

TL;DR

This study employs a nonequilibrium dynamical cluster approximation to analyze how short-range correlations influence the dynamics and thermalization behavior of the two-dimensional Falicov-Kimball model after an interaction quench, revealing nonthermal steady states with complex effective temperatures.

Contribution

It introduces a nonequilibrium DCA approach to study short-range correlations in the Falicov-Kimball model, highlighting nonthermal steady states and effective temperature complexities.

Findings

Thermalization is absent in DCA simulations, similar to single-site DMFT.

Nearest-neighbor charge correlations are larger in nonthermal steady states than in thermal states with the same energy.

Different energy intervals exhibit varying effective temperatures, including negative values.

Abstract

We use a nonequilibrium implementation of the dynamical cluster approximation (DCA) to study the effect of short-range correlations on the dynamics of the two-dimensional Falicov-Kimball model after an interaction quench. As in the case of single-site dynamical mean field theory, thermalization is absent in DCA simulations, and for quenches across the metal-insulator boundary, nearest-neighbor charge correlations in the nonthermal steady state are found to be larger than in the thermal state with identical energy. We investigate to what extent it is possible to define an effective temperature of the trapped state after a quench. Based on the ratio between the lesser and retarded Green's function we conclude that a roughly thermal distribution is reached within the energy intervals corresponding to the momentum-patch dependent subbands of the spectral function. The effectively different chemical potentials of these distributions however lead to a very hot, or even negative, effective temperature in the energy intervals between these subbands.