Nonequilibrium Criticality at the Onset of Time-Crystalline Order

TL;DR

This paper investigates the phase transitions leading to time-crystalline order in driven $O(N)$ models, revealing a new non-equilibrium universality class that governs long-distance physics regardless of microscopic equilibrium breaking.

Contribution

It identifies a novel non-equilibrium universality class for time-crystalline phase transitions using renormalization group analysis and $ ext{epsilon}$ expansion.

Findings

Discovery of a new non-equilibrium universality class.

Long-distance physics governed by this class regardless of microscopic details.

Application to magnon condensation in YIG films and exciton-polariton systems.

Abstract

We explore the phase transitions at the onset of time-crystalline order in $O(N)$ models driven out-of-equilibrium. The spontaneous breaking of time translation symmetry and its Goldstone mode are captured by an effective description with $O(N)\times SO(2)$ symmetry. Using the renormalization group and the $\epsilon=4-d$ expansion in a leading two-loop analysis, we identify a new non-equilibrium universality class. Strikingly, it controls the long-distance physics no matter how small the microscopic breaking of equilibrium conditions is. The $O(N=2)\times SO(2)$ symmetry group is realized for magnon condensation in pumped yttirum iron garnet (YIG) films and in exciton-polariton systems with a polarization degree of freedom.