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arXiv:1908.01959

Adiabatic dynamics of quasiperiodic transverse Ising model

B S Revathy, Uma Divakaran

Published Aug 6, 2019• 0 citations
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Abstract

We study the non-equilibrium dynamics due to slowly taking a quasiperiodic Hamiltonian across its quantum critical point. The special quasiperiodic Hamiltonian that we study here has two different types of critical lines belonging to two different universality classes, one of them being the well known quantum Ising universality class. In this paper, we verify the Kibble Zurek scaling which predicts a power law scaling of the density of defects generated as a function of the rate of variation of the Hamiltonian. The exponent of this power law is related to the equilibrium critical exponents associated with the critical point crossed. We show that the power-law behavior is indeed obeyed when the two types of critical lines are crossed, with the exponents that are correctly predicted by Kibble Zurek scaling.

DOI
10.48550/arxiv.1908.01959

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We study the non-equilibrium dynamics due to slowly taking a quasiperiodic Hamiltonian across its quantum critical point. The special quasiperiodic Hamiltonian that we study here has two different types of critical lines belonging to two different universality classes, one of them being the well known quantum Ising universality class. In this paper, we verify the Kibble Zurek scaling which predicts a power law scaling of the density of defects generated as a function of the rate of variation of the Hamiltonian. The exponent of this power law is related to the equilibrium critical exponents associated with the critical point crossed. We show that the power-law behavior is indeed obeyed when the two types of critical lines are crossed, with the exponents that are correctly predicted by Kibble Zurek scaling.
Abstract We study the non-equilibrium dynamics caused by slowly taking a quasiperiodic Hamiltonian across its quantum critical point. The special quasiperiodic Hamiltonian that we study here has two different types of critical lines belonging to two different universality classes, one of them being the well known quantum Ising universality class. In this paper, we verify the Kibble Zurek scaling which predicts a power law scaling of the density of defects generated as a function of the rate of variation of the Hamiltonian. The exponent of this power law is related to the equilibrium critical exponents associated with the critical point crossed. We show that the power-law behavior is indeed obeyed when the two types of critical lines are crossed, with the exponents that are correctly predicted by Kibble Zurek scaling.
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.
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.
Universality and scaling are fundamental concepts in equilibrium continuous phase transitions. Here, we unveil a unique and universal scaling behavior of the critical time in slowly driven dynamical quantum phase transition. Going beyond the analogy with equilibrium phase transition, we find that the critical time exhibits a power-law scaling with quenching rate and the scaling exponent is fully determined by underlining universality class. We explain this unique scaling behavior based on the adiabatic-impulse scenario in the Kibble-Zurek mechanism. This universal scaling behavior is verified to be valid not only in noninteracting single-particle system, but also in many-body interacting system, and not only in Hermitian system, but also in non-Hermitian system. Our study unravels a deep and fundamental relationship between dynamical phase transition and equilibrium phase tranition.
When a quantum phase transition is crossed in finite time, critical slowing down leads to the breakdown of adiabatic dynamics and the formation of topological defects. The average density of defects scales with the quench rate following a universal power law predicted by the Kibble-Zurek mechanism. We analyze the full counting statistics of kinks and report the exact kink number distribution in the transverse-field quantum Ising model. Kink statistics is described by the Poisson binomial distribution with all cumulants exhibiting a universal power law scaling with the quench rate. In the absence of finite-size effects, the distribution approaches a normal one, a feature that is expected to apply broadly in systems described by the Kibble-Zurek mechanism.