Linear Ramps of Interaction in the Fermionic Hubbard Model

TL;DR

This paper investigates the out-of-equilibrium dynamics of the Fermionic Hubbard Model during a linear ramp of interaction strength, revealing a dynamical phase transition and the effects of quantum fluctuations on relaxation processes.

Contribution

It introduces a combined approach using time-dependent Gutzwiller and $Z_2$ slave spin theories to analyze non-equilibrium dynamics and quantum fluctuation effects in the Hubbard Model during interaction ramps.

Findings

Existence of a dynamical phase transition during interaction ramps.

Quantum fluctuations significantly influence relaxation and the nature of the phase transition.

Scaling of excitation energy with ramp duration indicates non-adiabatic effects.

Abstract

We study the out of equilibrium dynamics of the Fermionic Hubbard Model induced by a linear ramp of the repulsive interaction $U$ from the metallic state through the Mott transition. To this extent we use a time dependent Gutzwiller variational method and complement this analysis with the inclusion of quantum fluctuations at the leading order, in the framework of a $Z_2$ slave spin theory. We discuss the dynamics during the ramp and the issue of adiabaticity through the scaling of the excitation energy with the ramp duration $\tau$. In addition, we study the dynamics for times scales longer than the ramp time, when the system is again isolated and the total energy conserved. We establish the existence of a dynamical phase transition analogous to the one present in the sudden quench case and discuss its properties as a function of final interaction and ramp duration. Finally we discuss the role of quantum fluctuations on the mean field dynamics for both long ramps, where spin wave theory is sufficient, and for very short ramps, where a self consistent treatment of quantum fluctuations is required in order to obtain relaxation.