# Quasi-Discrete Time Crystals in the Quasiperiodically Driven Lipkin–Meshkov–Glick Model

## TL;DR

This paper explores a new type of time crystal in a spin system driven by a non-repeating pattern, showing it can maintain ordered oscillations.

## Contribution

The study introduces quasi-discrete time crystals in a long-range interacting spin model under quasi-periodic driving.

## Key findings

- Quasi-discrete time crystal phases exhibit periodic magnetization oscillations under quasi-periodic driving.
- The system hosts analogs of period-doubling and higher-order DTCs with robustness to perturbations.
- The quasi-DTCs arise from all-to-all interactions and the recursive structure of the driving sequence.

## 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 quasi-periodic 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.