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

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 the dynamics of which 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, the main features of which are controlled by the universality class of the quantum transition. This requires a particular tuning of the dissipative interactions, the decay rate $u$ of which should scale as $u sim t_s^{−κ}$ 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.