Thermal melting of discrete time crystals: a dynamical phase transition induced by thermal fluctuations

Abstract

The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system composed of interacting spins, each of which couples to a thermal bath. It is shown that in the thermodynamic limit, even though the long-range temporary crystalline order is stable at low temperature, it is melting above a critical temperature, at which the system experiences a non-equilibrium phase transition. The critical behaviors of the continuous phase transition have been systematically investigated, and it is shown that despite the genuine non-equilibrium feature of such a periodically driven system, its critical properties fall into the 3D Ising universality class with a dynamical exponent ($z=2$) identical to that in the critical dynamics of kinetic Ising model without driving.

References in corpus (5)

• Absence of Quantum Time Crystals
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• General linearized theory of quantum fluctuations around arbitrary limit cycles

Cited by in corpus (7)

• Mode softening in time-crystalline transitions of open quantum systems
• Holographic dissipative space-time supersolids
• Prethermal time-crystalline spin ice and monopole confinement in a driven magnet
• Criticality and Rigidity of Dissipative Discrete Time Crystals in Solids
• Space-time symmetry breaking in nonequilibrium frustrated magnetism
• Emergence of spatial patterns and synchronization in superconducting time crystals
• The Sub-Exponential Critical Slowing Down at Floquet Time Crystal Phase Transition