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arXiv · 2208.11659

Dissipative time crystals with long-range Lindbladians

Gianluca Passarelli·Procolo Lucignano·Rosario Fazio·Angelo Russomanno
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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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Gianluca Passarelli, Procolo Lucignano, Rosario Fazio, Angelo Russomanno. 2022-08-24. Dissipative time crystals with long-range Lindbladians. https://doi.org/10.1103/physrevb.106.224308

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