Interaction-free ergodicity-breaking driven by temporally hyperuniform noise

Abstract

We show that norm-conserving spin models driven by temporally hyperuniform noise exhibit a sharp ergodicity-breaking transition in the absence of interactions. In the nonergodic phase, the dynamics freeze into configurations determined by the initial condition. Our analysis demonstrates that such interaction-free ergodicity breaking arises generically whenever a global constraint is imposed and the driving noise is class-I hyperuniform, the strongest form in Torquato's classification. The transition can also be interpreted as a condensation of fluctuations into the zero-frequency mode, reminiscent of Bose--Einstein condensation in an ideal gas.