Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions

• URL: http://arxiv.org/abs/2003.07604v1
• Date: Tue, 17 Mar 2020 10:01:39 GMT
• Title: Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions
• Authors: Davide Rossini, Ettore Vicari
• Abstract summary: We study the quantum dynamics of many-body systems, in the presence of dissipation, under Kibble-Zurek protocols. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven across the critical value of a zero-temperature quantum transition. In particular we address whether, and under which conditions, open quantum systems can develop a universal dynamic scaling regime similar to that emerging in closed systems. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation governing the time evolution of the system's density matrix. We argue that a dynamic scaling limit exists even in the presence of dissipation, whose main features are controlled by the universality class of the quantum transition. This requires a particular tuning of the dissipative interactions, whose decay rate $u$ should scale as $u\sim t_s^{-\kappa}$ with increasing the time scale $t_s$ of the KZ protocol, where the exponent $\kappa = z/(y_\mu+z)$ depends on the dynamic exponent $z$ and the renormalization-group dimension $y_\mu$ of the driving Hamiltonian parameter. Our dynamic scaling arguments are supported by numerical results for KZ protocols applied to a one-dimensional fermionic wire undergoing a quantum transition in the same universality class of the quantum Ising chain, in the presence of dissipative mechanisms which include local pumping, decay, and dephasing.

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