Dissipative time crystals with long-range Lindbladians

• URL: http://arxiv.org/abs/2208.11659v3
• Date: Wed, 21 Dec 2022 09:23:49 GMT
• Title: Dissipative time crystals with long-range Lindbladians
• Authors: Gianluca Passarelli, Procolo Lucignano, Rosario Fazio, Angelo Russomanno
• Abstract summary: We show that time-translation breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dissipative time crystals can appear in spin systems, when the $Z_2$ symmetry of the Hamiltonian is broken by the environment, and the square of total spin operator $S^2$ is conserved. In this manuscript, we relax the latter condition and show that time-translation-symmetry breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. We engineer an \textit{ad hoc} Lindbladian using power-law decaying spin operators and show that time-translation symmetry breaking appears when the decay exponent obeys $0<\eta\leq 1$. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points. We study the phase diagram and the magnetization dynamics in the mean-field approximation. We prove that this approximation is quantitatively accurate, when $0<\eta\leq1$ and the thermodynamic limit is taken, because the system does not develop sizable quantum fluctuations, if the Gaussian approximation is considered.

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