Clean two-dimensional Floquet time-crystal

• Published in: arXiv.org
• Main Authors: Santini, Alessandro, Santoro, Giuseppe E, Collura, Mario
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 27.09.2022
• Subjects: Decay rate; Ising model; Magnetic domains; Order parameters; Physics - Disordered Systems and Neural Networks; Physics - Quantum Gases; Physics - Quantum Physics; Physics - Statistical Mechanics; Stability; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2205.04865

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) pre-thermal 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 ordeblack phase at finite temperature. Interestingly, even for large deviations from the perfect spin flip, we observe a non-perturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.