# Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model

## TL;DR

This paper derives a quantum Boltzmann equation for the Mott insulator phase of the strongly interacting Fermi-Hubbard model, revealing momentum-dependent scattering and long-lived excitations, contrasting with weakly interacting systems.

## Contribution

It introduces a novel derivation of a Boltzmann equation for the strongly interacting Fermi-Hubbard model's Mott phase, highlighting momentum-dependent scattering effects.

## Key findings

- Scattering cross sections depend strongly on quasi-particle momenta.
- Excitations at the Mott gap minimum have vanishing scattering cross sections.
- Relaxation dynamics are significantly influenced by the excitation spectrum.

## Abstract

Via the hierarchy of correlations, we study the Mott insulator phase of the Fermi-Hubbard model in the limit of strong interactions and derive a quantum Boltzmann equation describing its relaxation dynamics. In stark contrast to the weakly interacting case, we find that the scattering cross sections strongly depend on the momenta of the colliding quasi-particles and holes. Therefore, the relaxation towards equilibrium crucially depends on the spectrum of excitations. For example, for particle-hole excitations directly at the minimum of the (direct) Mott gap, the scattering cross sections vanish such that these excitations can have a very long life-time.