Chaos as a manifestation of time-translation symmetry breaking
Phys. Rev. B 112, 134311 – Published 21 October, 2025
DOI: https://doi.org/10.1103/b6gq-z5nf
Abstract
While a generic open quantum system decays to its steady state, continuous time crystals (CTCs) develop spontaneous oscillation and never converge to a stationary state. Just as crystals develop correlations in space, CTCs do so in time. Here, we introduce a continuous quasi time crystals (CQTC). Despite being characterized by the presence of nondecaying oscillations, this phase does not retain its long-range order, making it time analogous to quasicrystal structures. We investigate the emergence of this phase in a minimal model, made of two coupled collective spin subsystems, each developing a CTC phase upon the action of a strong enough drive. The addition of a coupling enables the emergence of different synchronized phases, where both subsystems oscillate at the same frequency. In the transition between different CTC orders, the system develops chaotic dynamics with aperiodic oscillations. These chaotic features differ from those of closed quantum systems, as the dynamics is not characterized by a unitary evolution. We investigate the connection between chaos and this quasicrystalline phase using mean-field techniques, and we confirm these results by including quantum fluctuations at the lowest order.
