Exotic synchronization in continuous time crystals outside the symmetric subspace

TL;DR

This paper investigates the stability and dynamics of continuous time crystals outside the symmetric subspace, revealing multistability, exotic synchronization phenomena like chimera states, and nonlinear behaviors such as chaos in driven dissipative spin systems.

Contribution

It explores the effects of asymmetric subspaces on CTCs, uncovering multistability and complex synchronization regimes not previously studied.

Findings

Multistability and initial state dependence in CTC dynamics

Emergence of chimera and cluster synchronization states

Presence of oscillation death and chaos signatures

Abstract

Exploring continuous time crystals (CTCs) within the symmetric subspace of spin systems has been a subject of intensive research in recent times. Thus far, the stability of the time-crystal phase outside the symmetric subspace in such spin systems has gone largely unexplored. Here, we investigate the effect of including the asymmetric subspaces on the dynamics of CTCs in a driven dissipative spin model. This results in multistability, and the dynamics becomes dependent on the initial state. Remarkably, this multistability leads to exotic synchronization regimes such as chimera states and cluster synchronization in an ensemble of coupled identical CTCs. Interestingly, it leads to other nonlinear phenomena such as oscillation death and signature of chaos.