Quantum Boltzmann equation for strongly correlated systems: comparison to dynamical mean field theory

TL;DR

This paper introduces a quantum Boltzmann equation approach that neglects momentum conservation to model strongly correlated electron systems out of equilibrium, offering a computationally cheaper alternative to non-equilibrium DMFT with comparable insights.

Contribution

The paper proposes a simplified quantum Boltzmann equation method that approximates non-equilibrium dynamics in strongly correlated systems, validated against DMFT results.

Findings

Quantum Boltzmann equation captures key relaxation processes.

Method is computationally more efficient than non-equilibrium DMFT.

Applicable to complex systems and longer timescales.

Abstract

We investigate the potential of a quantum Boltzmann equation without momentum conservation for description of strongly correlated electron systems out of equilibrium. In a spirit similar to dynamical mean field theory (DMFT), the momentum conservation of the electron-electron scattering is neglected, which yields a time-dependent occupation function for the equilibrium spectral function, even in cases where well-defined quasiparticles do not exist. The main assumption of this method is that the spectral function remains sufficiently rigid under the non-equilibrium evolution. We compare the result of the quantum Boltzmann equation to non-equilibrium DMFT simulations for the case of photo-carrier relaxation in Mott insulators, where processes on very different timescales emerge, i.e., impact ionization, intra-Hubbard-band thermalization, and full thermalization. Since quantum Boltzmann simulations without momentum conservation are computationally cheaper than non-equilibrium DMFT, this method allows the simulation of more complicated systems or devices, and to access much longer times.