Liouvillian gap and out-of-equilibrium dynamics of a sunburst Kitaev ring: from local to uniform dissipation

• URL: http://arxiv.org/abs/2303.04207v2
• Date: Tue, 2 May 2023 14:02:28 GMT
• Title: Liouvillian gap and out-of-equilibrium dynamics of a sunburst Kitaev ring: from local to uniform dissipation
• Authors: Alessio Franchi, Francesco Tarantelli
• Abstract summary: We consider an open quantum system composed of a $(1+1)$-dimensional Kitaev ring coupled with the environment via $n$ particle-loss dissipators in a itsunburst geometry. We describe the out-of-equilibrium dynamics of the whole apparatus in terms of Lindblad master equations and focus on the scaling behavior of the Liovillian gap $Delta_lambda$ with the system size $L$.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider an open quantum system composed of a $(1+1)$-dimensional Kitaev ring coupled with the environment via $n$ particle-loss dissipators in a \textit{sunburst} geometry. We describe the out-of-equilibrium dynamics of the whole apparatus in terms of Lindblad master equations and focus on the scaling behavior of the Liovillian gap $\Delta_\lambda$ with the system size $L$. We unveil different regimes, which depend primarily on the number of dissipation sources considered in the large-size limit and the dissipation strength $w$, which may be either fixed or attenuated to zero as $w\sim1/L$. In the second part, we develop a dynamic Finite-Size Scaling framework close to Continuous Quantum Transitions to monitor the time evolution of the critical correlations and the entanglement entropy, emphasizing the role of $\Delta_\lambda$ in this regime.

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