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

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.

Figures (3)

• Figure 1: a) A quantum manybody system dynamics driven by a classical manybody system. The classical drive acts locally on the quantum manybody system. b) Illustrates a manybody lattice system with short range interactions coupled to a network of with arbitrary connectivity.
• Figure 2: a) Illustrates a one-dimensional quantum Ising chain with $N=30$ sites that is coupled to a network of $N=30$ phase oscillators with all-to-all coupling described by the Kuramoto model. b) Shows the time evolution of the transverse local fields $g_i(t)=G\cos[\theta_i(t)]$ and the emergence of synchronized motion. c) Depicts the instantaneous spectrum and the formation of two energy bands periodically oscillating in time. d) Shows the time evolution of a localized energy eigenstate of the Hamiltonian $\hat{H}(0)$. e) and f) Depict two snapshots of the eingenstates before ($J t=5$) and after ($J t=23$) synchronization. We have chosen parameters $G=3J$, $\tilde{K}=0.5J$, and $\omega=0.5J$.
• Figure 3: a) Illustrates a one-dimensional quantum Ising chain with $N=30$ sites that is coupled to a Kuramoto model in a zig-zag lattice with unidirectional coupling. b) Shows the time evolution of the transverse local fields $g_i(t)=G\cos[\theta_i(t)]$ and the emergence of travelling waves after the system synchronizes. c) Depicts the instantaneous spectrum and the emergence of three energy bands periodically oscillating in time. d) Shows the time evolution of a localized energy eigenstate of the Hamiltonian $\hat{H}(0)$ and how it is pumped along the lattice. e) and f) Depict two snapshots of the eingenstates before ($\omega t=50$) and after ($\omega t=150$) synchronization. We have chosen parameters $G=3J$, $K_1=0.2J$, $K_2=0.1J$, and $\omega=0.04J$