Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2406.18016

Universal scaling of quantum state transport in one-dimensional topological chain under nonadiabatic dynamics

Lingzi Huang, Menghua Deng, Chen Sun, Fuxiang Li

Published Jun 26, 2024• 0 citations
arXivHTMLPDF

Abstract

When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by Kibble-Zurek mechanism. In this study, we generalized this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependencies of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a novel perspective on quantum state transfer and enriches the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.

DOI
10.48550/arxiv.2406.18016

Related papers

Universal scaling of quantum state transport in a one-dimensional topological chain under nonadiabatic dynamics

Lingzi Huang, Menghua Deng, Chen Sun +1 more

When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by the Kibble-Zurek mechanism. In this study, we generalize this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependences of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a different perspective on quantum state transfer and enrich the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.

Physical review. B./Physical review. B•Jul 8, 2024•3 citations

Universal Dynamics of Inhomogeneous Quantum Phase Transitions: Suppressing Defect Formation

Fernando J. Gómez-Ruiz, Adolfo del Campo

In the nonadiabatic dynamics across a quantum phase transition, the Kibble-Zurek mechanism predicts that the formation of topological defects is suppressed as a universal power law with the quench time. In inhomogeneous systems, the critical point is reached locally and causality reduces the effective system size for defect formation to regions where the velocity of the critical front is slower than the sound velocity, favoring adiabatic dynamics. The reduced density of excitations exhibits a much steeper dependence on the quench rate and is also described by a universal power law that we demonstrated in a quantum Ising chain.

arXiv:1805.00525•Physical Review Letters•Mar 1, 2019•46 citations

Separation of the Kibble-Zurek Mechanism from Quantum Criticality

R. Jafari, Alireza Akbari

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.

cond-mat.stat-mechCross-listedarXiv:2602.19865•Physical Review Research•Feb 24, 2026•3 citations

Topological Defects from Quantum Reset Dynamics

R. Jafari, Henrik Johannesson, Sebastian Eggert

We analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale $τ$ of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as $τ$ increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.

cond-mat.stat-mechCross-listedarXiv:2602.00230•Physical review. B./Physical review. B•Feb 3, 2026•2 citations

Separation of the Kibble-Zurek mechanism from quantum criticality

Rouhollah Jafari, Alireza Akbari

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.

•May 13, 2026•0 citations

Defect Production across Higher-Order Phase Transitions beyond Kibble-Zurek Scaling

Menghua Deng, Zhoujian Sun, Fuxiang Li

The Kibble-Zurek mechanism predicts a universal scaling behavior of the defect production when a system is slowly quenched across a critical phase transition point. Here, we discover that the universal scaling behavior across a higher-order topological phase transition does not conform to the traditional Kibble-Zurek mechanism. To explain the anomalous scaling exponent, we develop a solvable Landau-Zener model that takes into account the role of topological edge band that dominates the phase transition. For a two-dimensional boundary-obstructed higher-order topological system, the Kibble-Zurek scaling must be modified to adopt the effective dimension of topological edge band instead of the real physical dimension. We also find that across the boundary-obstructed higher-order topological phase transition, boundary conditions can drastically modify the scaling behaviors. For comparison, we investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with physical dimension.

Physical Review Letters•Jan 7, 2025•10 citations
When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by Kibble-Zurek mechanism. In this study, we generalized this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependencies of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a novel perspective on quantum state transfer and enriches the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.
When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by the Kibble-Zurek mechanism. In this study, we generalize this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependences of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a different perspective on quantum state transfer and enrich the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.
In the nonadiabatic dynamics across a quantum phase transition, the Kibble-Zurek mechanism predicts that the formation of topological defects is suppressed as a universal power law with the quench time. In inhomogeneous systems, the critical point is reached locally and causality reduces the effective system size for defect formation to regions where the velocity of the critical front is slower than the sound velocity, favoring adiabatic dynamics. The reduced density of excitations exhibits a much steeper dependence on the quench rate and is also described by a universal power law that we demonstrated in a quantum Ising chain.
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 analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale τττ of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as τττ increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.
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.
The Kibble-Zurek mechanism predicts a universal scaling behavior of the defect production when a system is slowly quenched across a critical phase transition point. Here, we discover that the universal scaling behavior across a higher-order topological phase transition does not conform to the traditional Kibble-Zurek mechanism. To explain the anomalous scaling exponent, we develop a solvable Landau-Zener model that takes into account the role of topological edge band that dominates the phase transition. For a two-dimensional boundary-obstructed higher-order topological system, the Kibble-Zurek scaling must be modified to adopt the effective dimension of topological edge band instead of the real physical dimension. We also find that across the boundary-obstructed higher-order topological phase transition, boundary conditions can drastically modify the scaling behaviors. For comparison, we investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with physical dimension.