Dissipative time crystals originating from parity-time symmetry

Abstract

This study aims to provide evidence regarding the emergence of a class of dissipative time crystals when $\mathcal{P}\mathcal{T}$ symmetry of the systems is restored in collective spin systems with Lindblad dynamics. First, we show that a standard model of boundary time crystals (BTCs) satisfies the Liouvillian $\mathcal{P}\mathcal{T}$ symmetry, and prove that BTC exists only when the stationary state is $\mathcal{P}\mathcal{T}$ symmetric in the large-spin limit. Also, a similar statement is confirmed numerically for another BTC model. In addition, the mechanism of the appearance of BTCs is discussed through the development of a perturbation theory for a class of the one-spin models under weak dissipations. Consequently, we show that BTCs appear in the first-order correction when the total gain and loss are balanced. These results strongly suggest that BTCs are time crystals originating from $\mathcal{P}\mathcal{T}$ symmetry.

arXiv comment7+10 pages, 3+5 figures

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