A quantum Boltzmann equation for strongly correlated electrons

TL;DR

This paper derives a non-perturbative quantum Boltzmann equation for strongly correlated electrons, enabling the study of slow collective phenomena without relying on quasiparticle approximations.

Contribution

It introduces a quantum Boltzmann equation based on a non-perturbative scattering integral applicable to strongly correlated systems, extending non-equilibrium dynamical mean-field theory.

Findings

Formulation of a non-perturbative quantum Boltzmann equation

Evaluation of scattering integrals using non-equilibrium impurity models

Potential to study slow dynamical processes in correlated materials

Abstract

Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can potentially resolve this separation of timescales, but are often constructed within a perturbative framework. Here we derive a quantum Boltzmann equation which only assumes a separation of timescales (taken into account through the gradient approximation for convolutions in time), but is based on a non-perturbative scattering integral, and makes no assumption on the spectral function such as the quasiparticle approximation. In particular, a scattering integral corresponding to non-equilibrium dynamical mean-field theory is evaluated in terms of an Anderson impurity model in a non-equilibrium steady state with prescribed distribution functions. This opens the possibility to investigate dynamical processes in correlated solids with quantum impurity solvers designed for the study of non-equilibrium steady states.