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arXiv:1503.01512 · Physical Review B

Universal scaling for a quantum discontinuity critical point and quantum quenches

Sei Suzuki, Amit Dutta

Published Aug 24, 2015• 10 citations
arXivHTMLPDF

Abstract

We introduce the notion of a quantum version of a discontinuity critical point (DCP) in the context of a first-order quantum phase transition referred to as a quantum DCP (QDCP). We evaluate the critical exponents associated with such a QDCP using the appropriate scaling relations focusing mainly on a QDCP that is located at the boundary between a gapped phase and a gapless critical line as observed in a spin-$\frac{1}{2}$ XXZ chain while we also touch upon the conventional Ising case. We then study temporal and spatial quenches in the vicinity of the QDCP associated with the XXZ chain and propose the scaling relation for the defect density and the residual energy characterized by associated critical exponents. These predictions are numerically verified for quenches of the XXZ chain to the QDCP (or across it), thereby establishing the existence of a Kibble-Zurek scaling for such quenches given in terms of appropriate critical exponents. Finally, in the Appendix we consider a generic situation which reduces to the case when the QDCP separates two gapped phases and also to that occurring in the XXZ chain, and present detail analysis of the universality and scaling relations concerning quantum quenches.

DOI
10.1103/physrevb.92.064419

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We introduce the notion of a quantum version of a discontinuity critical point (DCP) in the context of a first-order quantum phase transition referred to as a quantum DCP (QDCP). We evaluate the critical exponents associated with such a QDCP using the appropriate scaling relations focusing mainly on a QDCP that is located at the boundary between a gapped phase and a gapless critical line as observed in a spin-12\frac{1}{2}21​ XXZ chain while we also touch upon the conventional Ising case. We then study temporal and spatial quenches in the vicinity of the QDCP associated with the XXZ chain and propose the scaling relation for the defect density and the residual energy characterized by associated critical exponents. These predictions are numerically verified for quenches of the XXZ chain to the QDCP (or across it), thereby establishing the existence of a Kibble-Zurek scaling for such quenches given in terms of appropriate critical exponents. Finally, in the Appendix we consider a generic situation which reduces to the case when the QDCP separates two gapped phases and also to that occurring in the XXZ chain, and present detail analysis of the universality and scaling relations concerning quantum quenches.
Understanding how noise influences nonequilibrium quantum critical dynamics is essential for both fundamental physics and the development of practical quantum technologies. While the quantum Kibble-Zurek (QKZ) mechanism predicts universal scaling during quenches across a critical point, real quantum systems exhibit complex decoherence that can substantially modify these behaviors, ranging from altering critical scaling to completely suppressing it. By considering a specific case of nondemolishing noise, we first show how decoherence can reshape universal scaling and verify these theoretical predictions using numerical simulations of spin chains across a wide range of noise strengths. Then, we study linear quenches in the transverse-field Ising model on IBM superconducting processors where the noise model is unknown. Using large system sizes of 80-120 qubits, we measure equal-time connected correlations, defect densities, and excess energies across various quench times. Surprisingly, unlike earlier observations where noise-induced defect production masked universal behavior at long times, we observe clear scaling relations, pointing towards persistent universal structure shaped by decoherence. The extracted scaling exponents differ from both ideal QKZ predictions and analytic results for simplified noise models, suggesting the emergence of a distinct noise-influenced universality regime. Our results, therefore, point toward the possibility of using universal dynamical scaling as a high-level descriptor of quantum hardware, complementary to conventional gate-level performance metrics.
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.
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.
We study the scaling of the decoherence factor of a qubit (spin-1/21/21/2) using the central spin model in which the central spin (qubit) is globally coupled to a transverse XY spin chain. The aim here is to study the nonequilibrium generation of decoherence when the spin chain is driven across (along) quantum critical points (lines) and derive the scaling of the decoherence factor in terms of the driving rate and some of the exponents associated with the quantum critical points. Our studies show that the scaling of the logarithm of the decoherence factor is identical to that of the defect density in the final state of the spin chain following a quench across isolated quantum critical points for both linear and nonlinear variations of a parameter, even if the defect density may not satisfy the standard Kibble-Zurek scaling. However, one finds an interesting deviation when the spin chain is driven along a critical line. Our analytical predictions are in complete agreement with numerical results. Our study, though limited to integrable two-level systems, points to the existence of a universality in the scaling of the decoherence factor which is not necessarily identical to the scaling of the defect density.
We consider the Rabi Hamiltonian, which exhibits a quantum phase transition (QPT) despite consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving an exact solution in the limit where the atomic transition frequency in the unit of the cavity frequency tends to infinity. The effect of a finite transition frequency is studied by analytically calculating finite-frequency scaling exponents as well as performing a numerically exact diagonalization. Going beyond this equilibrium QPT setting, we prove that the dynamics under slow quenches in the vicinity of the critical point is universal; that is, the dynamics is completely characterized by critical exponents. Our analysis demonstrates that the Kibble-Zurek mechanism can precisely predict the universal scaling of residual energy for a model without spatial degrees of freedom. Moreover, we find that the onset of the universal dynamics can be observed even with a finite transition frequency.
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.