Quasi-Discrete Time Crystals in the quasiperiodically driven Lipkin-Meshkov-Glick model

TL;DR

This paper explores how a Lipkin-Meshkov-Glick model under quasiperiodic Thue-Morse driving can host quasi-discrete time crystal phases, exhibiting persistent oscillations despite aperiodic driving, expanding understanding of non-equilibrium phases.

Contribution

It introduces the concept of quasi-discrete time crystals in a long-range interacting system under quasiperiodic drive, demonstrating robustness and novel phase behavior.

Findings

Quasi-DTC phases exhibit persistent magnetization oscillations.

The model supports period-doubling and higher-order quasi-DTCs.

Quasi-DTCs are stable against perturbations.

Abstract

A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin-Meshkov-Glick model under quasiperiodic Thue-Morse (TM) driving. Intriguingly, this infinite-range-interacting spin system can host ``quasi-discrete time crystal" (quasi-DTC) phases characterized by periodic oscillations of the magnetization. We demonstrate that our model can host the quasi-DTC analog of both period-doubling DTCs as well as higher-order DTCs. These quasi-DTCs are robust to various perturbations, and they originate from the interplay of ``all-to-all" interactions and the recursive structure of the TM sequence. Our results suggest that quasi-periodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems.