The Out-of-Equilibrium Time-Dependent Gutzwiller Approximation

TL;DR

This paper reviews an extension of the Gutzwiller approximation for out-of-equilibrium dynamics of correlated electrons, demonstrating its application to Hubbard model quenches and linking it to slave-spin theories for Mott transitions.

Contribution

It introduces a variational out-of-equilibrium Gutzwiller method applicable far beyond linear response, connecting it to spin-fermion models and Mott transition phenomena.

Findings

Predicts a dynamical phase transition in Hubbard model quenches.

Establishes a link between Gutzwiller approximation and slave-spin models.

Shows the method's applicability to multi-band and integer-filling systems.

Abstract

We review the recently proposed extension of the Gutzwiller approximation, M. Schiro' and M. Fabrizio, Phys. Rev. Lett. 105, 076401 (2010), designed to describe the out-of-equilibrium time-evolution of a Gutzwiller-type variational wave function for correlated electrons. The method, which is strictly variational in the limit of infinite lattice-coordination, is quite general and flexible, and it is applicable to generic non-equilibrium conditions, even far beyond the linear response regime. As an application, we discuss the quench dynamics of a single-band Hubbard model at half-filling, where the method predicts a dynamical phase transition above a critical quench that resembles the sharp crossover observed by time-dependent dynamical mean field theory. We next show that one can actually define in some cases a multi-configurational wave function combination of a whole set of mutually orthogonal Gutzwiller wave functions. The Hamiltonian projected in that subspace can be exactly evaluated and is equivalent to a model of auxiliary spins coupled to non-interacting electrons, closely related to the slave-spin theories for correlated electron models. The Gutzwiller approximation turns out to be nothing but the mean-field approximation applied to that spin-fermion model, which displays, for any number of bands and integer fillings, a spontaneous $Z_2$ symmetry breaking that can be identified as the Mott insulator-to-metal transition.