Transient phases and dynamical transitions in the post quench evolution of the generalized Bose-Anderson model

TL;DR

This paper investigates the real-time dynamics of the generalized Bose-Anderson model after a quench, revealing transient phases and a dynamical phase transition with persistent oscillations in the presence of dissipation.

Contribution

It provides a numerically exact analysis of post-quench dynamics in the N→∞ limit, uncovering long-lived transient phases and a novel dynamical phase transition.

Findings

Observation of long-lived transient phases during quenches crossing different phases.

Identification of a dynamical phase transition with persistent phase rotation.

Discussion of non-decaying modes in dissipative quantum systems.

Abstract

The exact description of the time evolution of open correlated quantum systems remains one of the major challenges of the condensed matter theory, specially for asymptotic long times where most numerical methods fail. Here, the post-quench dynamics of the $N$-component Bose-Anderson impurity model is studied in the $N\to\infty$ limit. The equilibrium phase diagram is similar to that of the Bose-Hubbard model in that it contains local versions of the Mott and Bose phases. Using a numerically exact procedure we are able to study the real time evolution including asymptotic long time regimes. The formation of long-lived transient phases is observed for quench paths crossing foreign phases. For quenches inside the local Bose condensed phase, a dynamical phase transition is reported, that separates the evolution towards a new equilibrium state and a regime characterized at large times by a persistent phase rotation of the order parameter. We explain how such non-decaying mode can exist in the presence of a dissipative bath. We discuss the extension of our results to the experimental relevant finite-$N$ case and their implication for the existence of non-decaying modes in generic quantum systems in the presence of a bath.