Periodically driven integrable systems with long-range pair potentials

Abstract

We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent $\alpha$. Starting from an initial unentangled state, we show that all local quantities relax to well-defined steady state values in the thermodynamic limit and after $n\gg 1$ drive cycles for any $\alpha$ and driving frequency $\omega$. We introduce a distance measure, ${\mathcal{D}}_l(n)$, that characterizes the approach of the reduced density matrix of a subsystem of $l$ sites to its final steady state. We chart out the $n$ dependence of ${\mathcal{D}}_l(n)$ and identify a critical value $\alpha ={\alpha }_c$ below which they generically decay to zero as $(\omega /n{)}^{1/2}$. For $\alpha >{\alpha }_c$, in contrast, ${\mathcal{D}}_l(n)\sim (\omega /n{)}^{3/2}[(\omega /n{)}^{1/2}]$ for $\omega \to \infty [0]$ with at least one intermediate dynamical transition. We also study the mutual information propagation to understand the nature of the entanglement spreading in space with increasing $n$ for such systems. We point out existence of qualitatively new features in the space-time dependence of mutual information for $\omega <{\omega }_c^{(1)}$, where ${\omega }_c^{(1)}$ is the largest critical frequency for the dynamical transition for a given $\alpha$. One such feature is the presence of {\it multiple} light cone-like structures which persists even when $\alpha$ is large. We also show that the nature of space-time dependence of the mutual information of long-ranged Hamiltonians with $\alpha \le 2$ differs qualitatively from their short-ranged counterparts with $\alpha >2$ for any drive frequency and relate this difference to the behavior of the Floquet group velocity of such driven system.

v2; two-column format, 19 pages, 16 figures (Shortened abstract due to character limit for arXiv submission; see main text); slightly modified version submitted for review

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• Dynamical relaxation of correlators in periodically driven integrable quantum systems
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• Dynamical relaxation behaviors of a critical quench
• Phase diagram of the disordered Kitaev chain with long range pairing connected to external baths
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• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
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• Order parameter dynamics of the non-linear sigma model in the large $N$ limit
• Slow decay rate of correlations induced by long-range extended Dzyaloshinskii-Moriya interactions
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• Preface: Long-range Interactions and Synchronization