Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity

TL;DR

This paper investigates the non-equilibrium dynamics of the Hubbard model after a sudden increase in interaction strength, revealing rapid thermalization of spectral functions and optical conductivity using advanced numerical methods.

Contribution

It introduces improved quantum Monte Carlo techniques within non-equilibrium dynamical mean-field theory and compares their accuracy to perturbation theory in studying spectral and transport properties.

Findings

Spectral functions show formation of Hubbard bands and a gap.

Rapid thermalization occurs at the transition between weak and strong coupling regimes.

Numerical methods accurately capture real-time dynamics up to certain timescales.

Abstract

We use non-equilibrium dynamical mean-field theory in combination with a recently developed Quantum Monte Carlo impurity solver to study the real-time dynamics of a Hubbard model which is driven out of equilibrium by a sudden increase in the on-site repulsion U. We discuss the implementation of the self-consistency procedure and some important technical improvements of the QMC method. The exact numerical solution is compared to iterated perturbation theory, which is found to produce accurate results only for weak interaction or short times. Furthermore we calculate the spectral functions and the optical conductivity from a Fourier transform on the finite Keldysh contour, for which the numerically accessible timescales allow to resolve the formation of Hubbard bands and a gap in the strongly interacting regime. The spectral function, and all one-particle quantities that can be calculated from it, thermalize rapidly at the transition between qualitatively different weak- and strong-coupling relaxation regimes.