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arXiv:2603.16709

Kibble-Zurek Mechanism in the Open Quantum Rabi Model

T. Pirozzi, G. Di Bello, V. Cataudella, C. A. Perroni, G. De Filippis

quant-phcond-mat.mes-hallSubmitted Mar 17, 2026• Announced Mar 18, 2026• 0 citations
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Abstract

The Kibble-Zurek mechanism provides a universal framework for predicting defect formation in non-equilibrium phase transitions. While Markovian dissipation typically degrades universal scaling, the impact of non-Markovian memory remains largely unexplored. We demonstrate that an Ohmic bath induces a Berezinskii-Kosterlitz-Thouless transition in the open quantum Rabi model. Using simulations based on Matrix Product States, we show that the excitation energy strictly follows universal Kibble-Zurek power-law scaling when evaluated at the freeze-out time. Crucially, we find that since the environment defines the universality class, dissipation does not inherently compete with adiabatic dynamics, in stark contrast to Markovian regimes. Our results establish the Kibble- Zurek mechanism as a robust witness of universality in open quantum systems, revealing that non-Markovian memory preserves the integrity of non-equilibrium scaling.

Comments
7 pages, 6 figures

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The Kibble-Zurek mechanism provides a universal framework for predicting defect formation in non-equilibrium phase transitions. While Markovian dissipation typically degrades universal scaling, the impact of non-Markovian memory remains largely unexplored. We demonstrate that an Ohmic bath induces a Berezinskii-Kosterlitz-Thouless transition in the open quantum Rabi model. Using simulations based on Matrix Product States, we show that the excitation energy strictly follows universal Kibble-Zurek power-law scaling when evaluated at the freeze-out time. Crucially, we find that since the environment defines the universality class, dissipation does not inherently compete with adiabatic dynamics, in stark contrast to Markovian regimes. Our results establish the Kibble- Zurek mechanism as a robust witness of universality in open quantum systems, revealing that non-Markovian memory preserves the integrity of non-equilibrium scaling.
We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws break down and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus nonadiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of nonlinear ramps and finite-size systems.
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.
When a system is swept through a quantum critical point (QCP), the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp time scale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a non-critical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality.
When a system is swept through a quantum critical point, the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp timescale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a noncritical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality. © 2026 authors. Published by the American Physical Society.
Non-Hermitian physics provides an effective description of open and nonequilibrium systems and hosts many novel and intriguing phenomena such as exceptional points and non-Hermitian skin effect. Despite extensive theoretical and experimental studies, however, how to properly deal with the nonadiabatic dynamics in driven non-Hermitian quantum system is still under debate. Here, we develop a theoretical framework based on time-dependent biorthogonal quantum formalism by redefining the associated state to obtain the gauge-independent transition probability, and study the nonadiabatic dynamics of a linearly driven non-Hermitian system. In contrast to the normalization method that leads to a modified Kibble-Zurek scaling behavior, our approach predicts that the defect production at exceptional points exhibits power-law scaling behaviors conforming to the Kibble-Zurek mechanism. In the fast quench regime, universal scaling behaviors are also found with respect to the initial quenching parameter, which can be explained by the impulse-adiabatic approximation. Moreover, as trespassing the PT -broken region, the phenomenon of defect freezing, i.e., violation of adiabaticity, is observed.
Abstract We study the dynamics of second-order phase transitions that may have taken place in the early universe and analyze the Kibble-Zurek (KZ) scaling as well as the formation of topological defects emerging from a quench in the one-dimensional Bose-Hubbard model. We describe the universal dynamics of the KZ mechanism (KZM) and the topological defect formation by simulating the Bose–Hubbard model at zero temperature. We study the effects of thermalization on the ground state by analyzing the transition between Mott and superfluid phases. The out-of-equilibrium dynamics induced by a quench of the hopping parameter is presented. We find a KZ scaling behaviour at zero temperature and analyze the KZ dynamics.