Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state

TL;DR

This paper investigates how periodically driven integrable systems generate entangled states with variable entanglement scaling, revealing dynamical phase transitions and steady state properties that depend on drive frequency and system dimension.

Contribution

It introduces a comprehensive analysis of entanglement scaling, dynamical phase transitions, and steady state features in driven integrable models across different dimensions.

Findings

Entanglement entropy exhibits a crossover from area to volume law.

Decays of entanglement entropy depend on drive frequency and number of cycles.

Dynamical phases are separated by a topological transition in the Floquet spectrum.

Abstract

We study a class of periodically driven $d-$dimensional integrable models and show that after $n$ drive cycles with frequency $\omega$, pure states with non-area-law entanglement entropy $S_n(l) \sim l^{\alpha(n,\omega)}$ are generated, where $l$ is the linear dimension of the subsystem, and $d-1 \le \alpha(n,\omega) \le d$. We identify and analyze the crossover phenomenon from an area ($S \sim l^{ d-1}$ for $d\geq1$) to a volume ($S \sim l^{d}$) law and provide a criterion for their occurrence which constitutes a generalization of Hastings' theorem to driven integrable systems in one dimension. We also find that $S_n$ generically decays to $S_{\infty}$ as $(\omega/n)^{(d+2)/2}$ for fast and $(\omega/n)^{d/2}$ for slow periodic drives; these two dynamical phases are separated by a topological transition in the eigensprectrum of the Floquet Hamiltonian. This dynamical transition manifests itself in the temporal behavior of all local correlation functions and does not require a critical point crossing during the drive. We find that these dynamical phases show a rich re-entrant behavior as a function of $\omega$ for $d=1$ models, and also discuss the dynamical transition for $d>1$ models. Finally, we study entanglement properties of the steady state and show that singular features (cusps and kinks in $d=1$) appear in $S_{\infty}$ as a function of $\omega$ whenever there is a crossing of the Floquet bands. We discuss experiments which can test our theory.