We consider the two-dimensional quantum Ising model, in absence of disorder, subject to periodic imperfect global spin flips. We show by a combination of exact diagonalization and tensor-network methods that the system can sustain a spontaneously broken discrete time-translation symmetry. Employing careful scaling analysis, we show the feasibility of a two-dimensional discrete time-crystal (DTC) prethermal phase. Despite an unbounded energy pumped into the system, in the high-frequency limit, a well-defined effective Hamiltonian controls a finite-temperature intermediate regime, wherein local time averages are described by thermal averages. As a consequence, the long-lived stability of the DTC relies on the existence of a long-range ordered phase at finite temperature. Interestingly, even for large deviations from the perfect spin flip, we observe a nonperturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.

Clean two-dimensional Floquet time crystal / Santini, A.; Santoro, G. E.; Collura, M.. - In: PHYSICAL REVIEW. B. - ISSN 2469-9969. - 106:13(2022), pp. 1-9. [10.1103/PhysRevB.106.134301]

Clean two-dimensional Floquet time crystal

Santini, A.;Santoro, G. E.;Collura, M.
2022-01-01

Abstract

We consider the two-dimensional quantum Ising model, in absence of disorder, subject to periodic imperfect global spin flips. We show by a combination of exact diagonalization and tensor-network methods that the system can sustain a spontaneously broken discrete time-translation symmetry. Employing careful scaling analysis, we show the feasibility of a two-dimensional discrete time-crystal (DTC) prethermal phase. Despite an unbounded energy pumped into the system, in the high-frequency limit, a well-defined effective Hamiltonian controls a finite-temperature intermediate regime, wherein local time averages are described by thermal averages. As a consequence, the long-lived stability of the DTC relies on the existence of a long-range ordered phase at finite temperature. Interestingly, even for large deviations from the perfect spin flip, we observe a nonperturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.
106
13
1
9
134301
https://arxiv.org/abs/2205.04865
Santini, A.; Santoro, G. E.; Collura, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/130476
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