Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice

TL;DR

This paper derives and numerically solves quantum Boltzmann equations for strongly interacting spinless fermions on a lattice, revealing unique relaxation dynamics dominated by particle-hole collisions in the strong-coupling limit.

Contribution

It introduces a novel derivation of quantum Boltzmann equations for strongly interacting fermions using the 1/Z-expansion and explores their relaxation behavior.

Findings

Particle-hole collisions dominate in the strong-coupling limit.

Relaxation times depend on initial excitation types.

Numerical simulations confirm the dominance of particle-hole interactions.

Abstract

Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium.The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z-expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation time scales strongly depend on the type of excitations (particles or holes or both) that are initially present.