The Out-of-Equilibrium Time-Dependent Gutzwiller Approximation

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.

25 pages. Proceedings of the Hvar 2011 Workshop on 'New materials for thermoelectric applications: theory and experiment'

References in corpus (9)

• Dynamical phase transition in correlated fermionic lattice systems
• Orbital selective Mott transition in multi-band systems: slave-spin representation and dynamical mean-field theory
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• Rotationally-invariant slave-boson formalism and momentum dependence of the quasiparticle weight
• Efficient implementation of the Gutzwiller variational method
• Equivalence of Gutzwiller and slave-boson mean-field theories for multi-band Hubbard models
• Gutzwiller description of non-magnetic Mott insulators: a dimer lattice model
• Dynamically Generated Double Occupancy as a Probe of Cold Atom Systems
• Sub-ohmic two-level system representation of the Kondo effect

Cited by in corpus (2)

• Thermal dynamics and electronic temperature waves in layered correlated materials
• Quantum fluctuations beyond the Gutzwiller approximation