Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems

TL;DR

This paper introduces a flexible variational approach using a time-dependent Gutzwiller wavefunction to study out-of-equilibrium dynamics in strongly correlated electron systems, revealing a dynamical transition in the Hubbard model.

Contribution

It presents a novel time-dependent variational method for analyzing quench dynamics in correlated electrons, extending mean field analysis to out-of-equilibrium situations.

Findings

Identifies a dynamical transition at half-filling in the Hubbard model.

Shows a crossover behavior at finite doping.

Demonstrates the method's ability to capture rich out-of-equilibrium phenomena.

Abstract

A simple and very flexible variational approach to the out-of-equilibrium quantum dynamics in strongly correlated electron systems is introduced through a time-dependent Gutzwiller wavefunction. As an application, we study the simple case of a sudden change of the interaction in the fermionic Hubbard model and find at the mean field level an extremely rich behaviour. In particular, a dynamical transition between small and large quantum quench regimes is found to occur at half-filling, in accordance with the analysis of Eckstein {\sl et al.}, Phys. Rev. Lett. {\bf 103}, 056403 (2009), obtained by dynamical mean field theory, that turns into a crossover at any finite doping.