Dynamical transitions and quantum quenches in mean-field models

TL;DR

This paper introduces a method to analyze quench dynamics in mean-field quantum models, revealing classical mappings and dynamical transitions that resemble phase transitions in fermionic systems.

Contribution

A generic approach to compute quench dynamics in fully connected quantum models, linking quantum evolution to classical effective dynamics and identifying novel dynamical transitions.

Findings

Quantum evolution maps onto classical effective dynamics.

Dynamical transitions occur at specific quench parameters.

Transitions are linked to singularities in classical dynamics.

Abstract

We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system. We apply our method to the Bose-Hubbard model, to a generalized Jaynes-Cummings model, and to the Ising model in a transverse field. We find that the quantum evolution can be mapped onto a classical effective dynamics, which involves only a few intensive observables. For some special parameters of the quench, peculiar dynamical transitions occur. They result from singularities of the classical effective dynamics and are reminiscent of the transition recently found in the fermionic Hubbard model. Finally, we discuss the generality of our results and possible extensions.