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.
Highlights
The recent experimental progress in the control and manipulation of quantum many-body systems has led to great achievements, opening the door for the realization of quantum simulators [1,2,3,4,5,6]
In the following we analyze the dynamic scaling behavior arising from dynamic protocols of quantum many-body systems in the presence of weak dissipation, evolving according to Eq (4), when the parameter μ is slowly varied across its critical value μc associated with the quantum transition driven by the Hamiltonian, starting from the gapped disordered phase, analogously to the standard KZ protocol for closed systems
We have investigated the interplay between coherent and dissipative drivings in the dynamics of quantum many-body systems subject to KZ protocols across continuous quantum transitions, starting from the gapped disordered phase, that is, when one Hamiltonian parameter is slowly driven across its critical value, for example, with a linear dependence on time
Summary
The recent experimental progress in the control and manipulation of quantum many-body systems has led to great achievements, opening the door for the realization of quantum simulators [1,2,3,4,5,6]. In the presence of weak dissipation, are still controlled by the universality class of the quantum transition, provided the system-environment interaction strength is suitably tuned This allows us to define a dynamic KZ scaling limit in the presence of dissipation. To check our general framework, we present a numerical analysis of KZ protocols applied to the fermionic Kitaev wire [43] across its quantum transition (belonging to the same universality class of the one appearing in quantum Ising chains) in the presence of dissipative mechanisms including local pumping, decay, and dephasing This model can be exactly and fully solved (i.e., with respect to its full excitation spectrum) even with a large number of sites, up to a few thousands, enabling us to perform an accurate numerical investigation of the dynamic KZ scaling behavior put forward.
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