Prethermalization in periodically-driven nonreciprocal many-body spin systems

TL;DR

This paper explores prethermalization in high-frequency driven nonreciprocal classical spin systems, revealing long-lived metastable states and proposing an extended Hamiltonian framework to understand their dynamics.

Contribution

It introduces a novel class of nonreciprocal, phase-space-volume-preserving spin dynamics without a Hamiltonian, and extends the concept of prethermalization to these systems.

Findings

Metastable magnetization plateau with duration scaling as the fourth power of drive frequency

Lack of an effective Hamiltonian prevents canonical ensemble description of the prethermal state

Hamiltonian extension with auxiliary degrees of freedom demonstrates symplecticity breaking at high frequency

Abstract

We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the dynamics of the system cannot be derived from any time-dependent Hamiltonian. In the high-frequency limit, we find that the magnetization dynamics features a long-lived metastable plateau, whose duration is controlled by the fourth power of the drive frequency. However, due to the lack of an effective Hamiltonian, the prethermal state the system evolves into cannot be understood within the framework of the canonical ensemble. We propose a Hamiltonian extension of the system using auxiliary degrees of freedom, in which the original spins constitute an open yet nondissipative subsystem. This allows us to perturbatively derive effective equations of motion that manifestly display symplecticity breaking at leading order in the inverse frequency. We thus extend the notion of prethermal dynamics, observed in the high-frequency limit of periodically-driven systems, to nonreciprocal systems.