Dynamical Transition for a class of integrable models coupled to a bath

TL;DR

This paper investigates how coupling integrable models to different types of baths affects their dynamical phase transitions under periodic driving, revealing preserved transitions with fermionic baths and exponential decay with bosonic baths.

Contribution

It provides a semi-analytic framework for understanding the impact of system-bath coupling on dynamical phase transitions in integrable models under periodic drive.

Findings

Fermionic baths preserve the dynamical transition and power-law decay.

Bosonic baths induce exponential decay after a critical number of drive cycles.

Power-law behavior persists below the critical drive cycles even with system-bath coupling.

Abstract

We study the dynamics of correlation functions of a class of $d-$dimensional integrable models coupled linearly to a fermionic or bosonic bath in the presence of a periodic drive with a square pulse protocol. It is well known that in the absence of the bath, these models exhibit a dynamical phase transition; all correlators decay to their steady state values as $n_0^{-(d+1)/2}$[$n_0^{-d/2}]$ above [below] a critical frequency $\omega_c$, where $n_0$ is the number of drive cycles. We find that the presence of a linearly coupled fermionic bath which maintains integrability of the system preserves this transition. We provide a semi-analytic expression for the evolution operator for this system and use it to provide a phase diagram showing the different dynamical regimes as a function of the system-bath coupling strength and the bath parameters. In contrast, when such models are coupled to a bosonic bath which breaks integrability of the model, we find exponential decay of the correlators to their steady state. Our numerical analysis shows that this exponential decay sets in above a critical number of drive cycles $n_c$ which depends on the system-bath coupling strength and the amplitude of perturbation. Below $n_c$, the system retains the power-law behavior identical to that for the closed integrable models and the dynamical transition survives. We discuss the applicability of our results for interacting fermion systems and discuss experiments which can test our theory.