Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model

TL;DR

This paper explores how self-organized classical drives influence quantum spin chains, revealing emergent symmetries and topological behaviors, with potential for experimental realization in quantum devices.

Contribution

It introduces a framework for understanding quantum dynamics under self-organized, non-periodic drives, demonstrating emergent symmetries and topological effects in spin chains coupled to classical models.

Findings

Kuramoto-driven spin chains reach periodic steady states with emergent symmetries.

Time-periodic steady states exhibit translational symmetry and topological properties.

Potential for experimental implementation in near-term quantum devices.

Abstract

Floquet theory is a widely used framework to describe the dynamics of periodically-driven quantum systems. The usual set up to describe such kind of systems is to consider the effect of an external control with a definite period in time that can act either globally or locally on the system of interest. However, besides the periodicity, there is no classical correlation or other well defined structures in the drive. In this work, we consider drives that exhibit self-organization phenomena reaching periodic steady states with emergent symmetries. To substantiate our results, we consider two examples of a one-dimensional quantum spin chains in a transverse field coupled to a classical Kuramoto model. In the case of all-to-tall coupling, the Kuramoto model drives the Ising chain into a time-periodic steady state with an emergent translational symmetry. For a Kuramoto model in a Zig-zag lattice, the XX spin chain is trimerized and the dynamics exhibit topological behavior that can be exploited to perform topological pumping. Our results can be experimentally implemented in near-term quantum devices in digital and analog platforms.