Quantum Quenches in the Hubbard Model: Time Dependent Mean Field Theory and The Role of Quantum Fluctuations

TL;DR

This paper investigates the non-equilibrium dynamics of the fermionic Hubbard model after a sudden interaction change, using a time-dependent variational approach and analyzing quantum fluctuations beyond mean field.

Contribution

It introduces a novel time-dependent variational method for the Hubbard model and explores the impact of quantum fluctuations on non-equilibrium dynamics.

Findings

Identifies a sharp transition between oscillation regimes at half filling.

Quantum fluctuations become massless and unstable before the mean field critical line.

Doping turns the transition into a crossover, reducing sharp non-equilibrium features.

Abstract

We study the non equilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map the model onto an auxiliary Quantum Ising Model in a transverse field coupled to free fermionic quasiparticles. Remarkably, the Gutzwiller approximation turns out to correspond to the mean field decoupling of this model in the limit of infinite coordination lattices. The advantage is that we can go beyond mean field and include gaussian fluctuations around the non equilibrium mean field dynamics. Unlike at equilibrium, we find that quantum fluctuations become massless and eventually unstable before the mean field dynamical critical line, which suggests they could even alter qualitatively the mean field scenario.