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arXiv:2610.13033

When irrelevance governs: dissipation-regression scaling in open quantum criticality

Fan Zhong

quant-phcond-mat.stat-mechSubmitted Oct 9, 2026• Announced Oct 12, 2026• 0 citations
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Abstract

The real-time dynamics of quantum phase transitions in open systems coupled to finite-temperature environments sits at the heart of contemporary condensed-matter and quantum-information science. Here, invoking a Schwinger-Keldysh formalism, we uncover that, within the coherence-dominated regime of critical real-time evolution, a dissipative coupling deemed naively irrelevant determines, counterintuitively, the longest timescale that holds sway. Possessing a well-defined temporal scaling dimension, it engenders a novel dissipation-regression scaling that systematically reproduces the unusual Kibble-Zurek scaling and relaxation observed in recent numerical studies. By contrast, dissipation-dominated dynamics behaves qualitatively differently. There, furthermore, we show that the discretized and diagonalized formulations of the same open quantum Ising chain realize distinct universality classes.

Comments
10 pages, no figure. Substantially extended from 2607.11206v1

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The real-time dynamics of quantum phase transitions in open systems coupled to finite-temperature environments sits at the heart of contemporary condensed-matter and quantum-information science. Here, invoking a Schwinger-Keldysh formalism, we uncover that, within the coherence-dominated regime of critical real-time evolution, a dissipative coupling deemed naively irrelevant determines, counterintuitively, the longest timescale that holds sway. Possessing a well-defined temporal scaling dimension, it engenders a novel dissipation-regression scaling that systematically reproduces the unusual Kibble-Zurek scaling and relaxation observed in recent numerical studies. By contrast, dissipation-dominated dynamics behaves qualitatively differently. There, furthermore, we show that the discretized and diagonalized formulations of the same open quantum Ising chain realize distinct universality classes.
Probing, understanding, predicting, and controlling the real-time dynamics of quantum phase transitions in open systems are of pivotal importance to modern condensed matter physics, statistical physics, and quantum computing, among others. Here it is argued that a distinct temporal renormalization-group eigenvalue is needed for quantum criticality in open systems weakly coupled to their finite-temperature environment. This new physics enables the formulation of a general scaling theory that can accurately account for the critical properties including the specific Kibble-Zurek scaling in such open quantum systems. Remarkably, the critical exponents of time-related quantities are altered nonperturbatively regardless of how weak the coupling is, except for an Ohmic bath. Perspectives for future study are also discussed.
Taking the quantum Kitaev chain as an example, we have studied the universal dynamical behaviors resulting from quantum criticality under the condition of environmental temperature quench. Our findings reveal that when the quantum parameter is at its critical value, both the excess excitation density at the end of linear quench and the free relaxation exhibit universal scaling behaviors. The scaling laws observed upon quenching to the zero-temperature quantum critical point and nonzero temperature points exhibit distinct scaling exponents, which are all intimately related to the dynamical critical exponents of the quantum phase transition. Additionally, for the case of linear quench to finite temperatures, we have also discovered an intrinsic universal dynamical behavior that is independent of quantum criticality. Our research offers profound insights into the relationship between quantum criticality and nonequilibrium dynamics from two perspectives: Kibble-Zurek-like scaling behavior and free relaxation dynamics. Notably, the Kibble-Zurek-like scaling behavior in this context differs from the standard Kibble-Zurek mechanism. These two aspects jointly open up a new avenue for us to understand quantum criticality through real-time dynamical behavior, even at finite temperatures.
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.
The Dicke model is a paradigmatic setting for collective light-matter physics and the superradiant phase transition. Yet extracting the critical exponents is challenging at experimentally accessible mesoscopic sizes, due to the slow divergence of the correlation time under all-to-all coupling and a photon-loss-driven crossover to a distinct dissipative universality class. Here, we perform a large-NNN analysis that identifies distinct coherent and dissipative fixed points for the closed and open Dicke models. We then develop a unified mesoscopic scaling framework that incorporates the leading irrelevant correction and, going beyond static and spectral probes, brings ramping dynamics under the same scaling description. It recovers the corresponding exponents, verifies Kibble-Zurek scaling, and clarifies how finite size, dissipation, and speed compete in the ramping dynamics. Our work thus establishes a unified framework for resolving static and dynamical critical scaling in closed and open quantum systems, with broader applicability to mesoscopic systems with long-range interactions.
We study finite-time driving across second-order dissipative quantum phase transitions described by Lindblad dynamics. We show that the nonadiabatic entropy production, which quantifies deviations from the instantaneous nonequilibrium steady state, exhibits universal power-law scaling with the ramp duration in analogy to the Kibble-Zurek mechanism for closed systems. This establishes the universality of irreversible dissipation induced by driving an open quantum system near criticality. Furthermore, in systems described by bosonic Gaussian states, our scaling laws predict that the nonadiabatic entropy production is independent of driving speed to leading order, revealing a distinctive feature of Gaussian dissipative quantum phase transitions. We validate these analytical predictions in the thermodynamic limit of the driven-dissipative Dicke model and via finite-size scaling in the open Kerr model. Our results establish a general framework for understanding universal nonequilibrium response and thermodynamic irreversibility in critical open quantum systems.