Exotic Synchronization in Continuous Time Crystals Outside the Symmetric Subspace

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Nonlinear Systems

Background:

• Continuous time crystals (CTCs) are a novel phase of matter exhibiting periodic behavior in time.
• Research has primarily focused on CTCs within the symmetric subspace of spin systems.
• The stability and dynamics of CTCs outside the symmetric subspace remain largely unexplored.

Purpose of the Study:

• To investigate the effect of asymmetric subspaces on the dynamics of continuous time crystals (CTCs).
• To explore emergent phenomena in driven dissipative spin systems when including asymmetric subspaces.
• To analyze the impact of multistability on synchronization and nonlinear dynamics in ensembles of CTCs.

Main Methods:

• Theoretical investigation of a driven dissipative spin model.
• Inclusion of asymmetric subspaces in the analysis of CTC dynamics.
• Examination of coupled identical CTCs to study synchronization regimes.

Main Results:

• The inclusion of asymmetric subspaces leads to multistability in CTC dynamics.
• Dynamics become dependent on the initial state of the system.
• Exotic synchronization regimes, including chimera states and cluster synchronization, emerge in coupled CTCs.
• Other nonlinear phenomena like oscillation death and signatures of chaos are observed.

Conclusions:

• Asymmetric subspaces significantly alter CTC dynamics, introducing multistability and initial state dependence.
• The study reveals novel synchronization patterns and nonlinear phenomena in driven dissipative spin systems.
• This work expands the understanding of CTCs beyond the symmetric subspace, opening new avenues for research.