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

Area of Science:

• Quantum physics
• Condensed matter physics
• Non-equilibrium statistical mechanics

Background:

• Discrete time crystals (DTCs) exhibit persistent sub-harmonic oscillations in periodically driven systems.
• Investigating temporal order under aperiodic driving is crucial for understanding non-equilibrium phases of matter.

Purpose of the Study:

• To explore the possibility of temporal periodic order persisting under aperiodic driving.
• To investigate the dynamics of a Lipkin-Meshkov-Glick model under quasi-periodic Thue-Morse driving.

Main Methods:

• Utilized a Lipkin-Meshkov-Glick model with infinite-range interactions.
• Applied quasi-periodic Thue-Morse (TM) driving protocols.
• Analyzed the emergence of "quasi-discrete time crystal" (quasi-DTC) phases.

Main Results:

• Discovered quasi-DTC phases characterized by periodic magnetization oscillations in the spin system.
• Demonstrated the existence of quasi-DTC analogs to period-doubling and higher-order DTCs.
• Showed these quasi-DTCs are robust to perturbations and arise from "all-to-all" interactions and TM sequence recursion.

Conclusions:

• Quasi-periodic driving offers a viable route to realizing novel non-equilibrium phases.
• Long-range interacting systems can host robust quasi-DTC phases.
• The interplay between interactions and driving sequence structure is key to novel phase emergence.