Critical behavior of a programmable time-crystal lattice gas

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Non-equilibrium Systems

Background:

• Time crystals exhibit spontaneous breaking of time-translation symmetry, leading to robust periodic motion.
• Previous hydrodynamic studies demonstrated the induction of time-crystalline order using external fields in driven diffusive fluids.
• Understanding the microscopic origins and universality classes of these emergent phenomena is crucial.

Purpose of the Study:

• To analyze the emergence of time-crystalline order at the microscopic level in a generalized exclusion process.
• To characterize the non-equilibrium phase transitions to higher-order time-crystal phases (m > 1).
• To determine the universality class and critical exponents associated with these transitions.

Main Methods:

• Utilized extensive Monte Carlo simulations on a 'time-crystal lattice gas' model.
• Characterized the phase transition by analyzing the order parameter, susceptibility, and Binder cumulant.
• Measured critical exponents and elucidated condensate density profiles and velocities.

Main Results:

• Identified and characterized non-equilibrium phase transitions to complex time-crystal phases for various orders (m).
• Measured critical exponents that fall within the Kuramoto universality class, indicating synchronization behavior.
• Confirmed a predicted scaling property for higher-order condensate shapes relative to first-order ones.

Conclusions:

• The microscopic analysis confirms the spontaneous emergence of time-crystalline order in the studied lattice gas model.
• The observed universality class suggests a connection between time-crystal formation and oscillator synchronization phenomena.
• This work provides a promising microscopic route for creating and controlling time crystals.