Scaling behavior of quantum critical relaxation dynamics in a heat bath

Abstract

We study the scaling behavior of the relaxation dynamics to thermal equilibrium when a quantum system is near the quantum critical point. In particular, we investigate systems whose relaxation dynamics is described by a Lindblad master equation. We find that the universal scaling behavior not only exhibits in the equilibrium stage at the long-time limit, but also manifests itself in the non-equilibrium relaxation process. While the critical behavior is dictated by the low-lying energy levels of the Hamiltonian, the dissipative part in the Lindblad equation also plays important roles in two aspects: First, the dissipative part makes the high energy levels decay fast after which the universal behavior controlled by the low-lying modes emerges. Second, the dissipation rate gives rise to a time scale that affects the scaling behavior. We confirm our theory by solving the Lindblad equation for the one-dimensional transverse-field Ising model.

arXiv comment5 pages, 4 figures

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• Dissipative dynamics at first-order quantum transitions
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• Out-of-equilibrium dynamics arising from slow round-trip variations of Hamiltonian parameters across quantum and classical critical points
• Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures
• Dynamical relaxation behaviors of a critical quench
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
• Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
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