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Bulletin of the American Physical Society

Critical phenomena and the universality of the Kibble-Zurek mechanism in driven dissipative systems

Hil Fung Harry Cheung, Yogesh Sharad Patil, Tamiro Villazon, Aditya Date, Anushya Chandran, Anatoli Polkovnikov, Mukund Vengalattore

Published May 29, 2018• 0 citations
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In this paper we address the question how the Kibble-Zurek mechanism, which describes the formation of topological defects in quantum systems subjected to a quench across a critical point, is generalized to the same scenario but for driven-dissipative quantum critical systems. In these out of equilibrium systems, the critical behavior is manifested in the steady states rather than in the ground states as in quantum critical models of closed systems. To give the generalization we need to establish what is meant by adiabaticity in open quantum systems. Another most crucial concept that we clarify is the characterization of non-adiabatic excitations. It is clear what these are for a Hamiltonian systems, but question is more subtle for driven-dissipative systems. In particular, the important observation is that the instantaneous steady states serve as reference states. From these the excitations can then be extracted by comparing the distance from the evolved state to the instantaneous steady state. With these issues resolved we demonstrate the applicability of the generalized Kibble-Zurek mechanism to an open Landau-Zener problem and show universal Kibble-Zurek scaling for an open transverse Ising model. Thus, our results support any assumption that non-equilibrium quantum critical behavior can be understood from universal features.
We study the driven dynamics across the critical points of the Yang-Lee edge singularities (YLESs) in a finite-size quantum Ising chain with an imaginary symmetry-breaking field. In contrast to the conventional classical or quantum phase transitions, these phase transitions are induced by tuning the strength of the dissipation in a non-Hermitian system and can occur even at finite size. For conventional phase transitions, universal behaviors in driven dynamics across critical points are usually described by the Kibble-Zurek mechanism, which states that the scaling in dynamics is dictated by the critical exponents associated with one critical point and topological defects will emerge after the quench. While the mechanism leading to topological defects breaks down in the YLES, we find that for small lattice size, the driven dynamics can still be described by the Kibble-Zurek scaling with the exponents determined by the (0+1)-dimensional YLES. For medium finite size, however, the driven dynamics can be described by the Kibble-Zurek scaling with two sets of critical exponents determined by both the (0+1)-dimensional and the (1+1)-dimensional YLESs.
The conventional Kibble-Zurek mechanism and the finite-time scaling provide universal descriptions of the driven critical dynamics from gapped initial states based on the adiabatic-impulse scenario. Here we investigate the driven critical dynamics in two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases separated by the quantum critical point triggered by the interplay between fluctuations of gapless Dirac fermions and order parameter bosons. We find that despite the existence of the gapless initial phase, the driven dynamics can still be captured by the finite-time scaling form. This leads us to propose a criterion for the validity of Kibble-Zurek mechanism with a gapless initial state. Accordingly, our results generalize the Kibble-Zurek theory to incorporate composite fluctuations and relax its requirement for a gapped initial state to systems accommodating gapless Dirac fermionic excitations. Our work not only brings fundamental perspective into the nonequilibrium critical dynamics, but also provides an approach to fathom quantum critical properties in fermionic systems. The Kibble-Zurek mechanism and finite-time scaling provide descriptions of the driven critical dynamics from gapped initial states. Here, the authors generalize these theories to Dirac systems accommodating gapless initial states.