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

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.

15 pages, 8 figures

References in corpus (10)

• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Adiabatic dynamics in open quantum critical many-body systems
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Finite-size scaling at first-order quantum transitions
• Work statistics across a quantum phase transition
• Robustness of adiabatic passage trough a quantum phase transition
• Anti-Kibble-Zurek behavior of a noisy transverse-field XY chain and its quantum simulation with two-level systems
• Scaling of decoherence and energy flow in interacting quantum spin systems

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