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:1612.02259 · Scientific Reports

Quantum Critical Scaling under Periodic Driving

Salvatore Lorenzo, Jamir Marino, Francesco Plastina, G. Massimo Palma, Tony J. G. Apollaro

Published Jul 12, 2017• 30 citations
arXivHTMLPDF

Abstract

Abstract Universality is key to the theory of phase transitions, stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model’s microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time τ bd , proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving.

DOI
10.1038/s41598-017-06025-1

Related papers

Quantum Critical Scaling under Periodic Driving

Salvatore Lorenzo, Jamir Marino, Francesco Plastina +2 more

Universality is key to the theory of phase transitions, stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time tbd, proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving.

•Jan 1, 2017•18 citations

Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Tony J. G. Apollaro, Salvatore Lorenzo

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

arXiv:1810.01825•Italian Quantum Information Science Conference (IQIS)•Jun 25, 2019•0 citations

Critical behaviour of the quasi-periodic quantum Ising chain

Philip J. D. Crowley, Chris R. Laumann, Anushya Chandran

Abstract The interplay of correlated spatial modulation and symmetry breaking leads to quantum critical phenomena intermediate between those of the clean and randomly disordered cases. By performing a detailed analytic and numerical case study of the quasi-periodically (QP) modulated transverse field Ising chain, we provide evidence for the conjectures of reference (Crowley et al 2018 Phys. Rev. Lett. 120 175702) regarding the QP-Ising universality class. In the generic case, we confirm that the logarithmic wandering coefficient w governs both the macroscopic critical exponents and the energy-dependent localisation length of the critical excitations. However, for special values of the phase difference Δ between the exchange and transverse field couplings, the QP-Ising transition has different properties. For Δ = 0, a generalised Aubry–André duality prevents the finite energy excitations from localising despite the presence of logarithmic wandering. For Δ such that the fields and couplings are related by a lattice shift, the wandering coefficient w vanishes. Nonetheless, the presence of small couplings leads to non-trivial exponents and localised excitations. Our results add to the rich menagerie of quantum Ising transitions in the presence of spatial modulation.

arXiv:1812.01660•Journal of Statistical Mechanics Theory and Experiment•Aug 1, 2022•8 citations

Universal short-time quantum critical dynamics in imaginary time

Shuai Yin, Peizhi Mai, Fan Zhong

We propose a scaling theory for the universal imaginary-time quantum critical dynamics for both short and long times. We discover that there exists a universal critical initial slip related to a small initial order parameter ${M}_{0}$. In this stage, the order parameter $M$ increases with the imaginary time $\ensuremath{\tau}$ as $M\ensuremath{\propto}{M}_{0}{\ensuremath{\tau}}^{\ensuremath{\theta}}$ with a universal initial-slip exponent $\ensuremath{\theta}$. For the one-dimensional transverse-field Ising model, we estimate $\ensuremath{\theta}$ to be $0.373$, which is markedly distinct from its classical counterpart. Apart from the local order parameter, we also show that the entanglement entropy exhibits universal behavior in the short-time region. As the critical exponents in the early stage and in equilibrium are identical, we apply the short-time dynamics method to determine quantum critical properties. The method is generally applicable in both the Landau-Ginzburg-Wilson paradigm and topological phase transitions.

arXiv:1311.0108•Physical Review B•Apr 30, 2014•28 citations

Dynamic phase transition in the three-dimensional kinetic Ising model in an oscillating field

Hyunhang Park, Michel Pleimling

Using numerical simulations, we investigate the properties of the dynamic phase transition that is encountered in the three-dimensional Ising model subjected to a periodically oscillating magnetic field. The values of the critical exponents are determined through finite-size scaling. Our results show that the studied nonequilibrium phase transition belongs to the universality class of the equilibrium three-dimensional Ising model.

arXiv:1303.2157•Physical Review E•Mar 20, 2013•50 citations

Universality and Dynamic Localization in Kibble-Zurek of the Quantum Ising Model

Michael Kolodrubetz

Recent work has suggested that the Kibble-Zurek mechanism can be re-interpreted as a theory of critical scaling out of equilibrium. While this has been shown for some classical and integrable models, in this work we demonstrate one crucial aspect of critical scaling theory: universality. We solve for the time-dependent finite-size scaling functions of the 1D transversefield Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally-studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and show that they should be robustly observable within present cold atom experiments. In addition, we discuss recent results in which the Ising model is extended by imbuing the magnetic field with dynamics. We predict using Kibble-Zurek scaling and numerically confirm that the magnetic field ramp is dynamically arrested at the quantum critical point. Extensions of this theory indicate that dynamic localization near critical points should be omnipresent in nature, and may have implications in particle physics as a possible mechanism for giving the Higgs boson a light mass.

Bulletin of the American Physical Society•Mar 7, 2014•0 citations
Abstract Universality is key to the theory of phase transitions, stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model’s microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time τ bd , proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving.
Universality is key to the theory of phase transitions, stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time tbd, proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving.
The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.
Abstract The interplay of correlated spatial modulation and symmetry breaking leads to quantum critical phenomena intermediate between those of the clean and randomly disordered cases. By performing a detailed analytic and numerical case study of the quasi-periodically (QP) modulated transverse field Ising chain, we provide evidence for the conjectures of reference (Crowley et al 2018 Phys. Rev. Lett. 120 175702) regarding the QP-Ising universality class. In the generic case, we confirm that the logarithmic wandering coefficient w governs both the macroscopic critical exponents and the energy-dependent localisation length of the critical excitations. However, for special values of the phase difference Δ between the exchange and transverse field couplings, the QP-Ising transition has different properties. For Δ = 0, a generalised Aubry–André duality prevents the finite energy excitations from localising despite the presence of logarithmic wandering. For Δ such that the fields and couplings are related by a lattice shift, the wandering coefficient w vanishes. Nonetheless, the presence of small couplings leads to non-trivial exponents and localised excitations. Our results add to the rich menagerie of quantum Ising transitions in the presence of spatial modulation.
We propose a scaling theory for the universal imaginary-time quantum critical dynamics for both short and long times. We discover that there exists a universal critical initial slip related to a small initial order parameter M0{M}_{0}M0​. In this stage, the order parameter MMM increases with the imaginary time $\ensuremath{\tau}$ as $M\ensuremath{\propto}{M}_{0}{\ensuremath{\tau}}^{\ensuremath{\theta}}$ with a universal initial-slip exponent $\ensuremath{\theta}$. For the one-dimensional transverse-field Ising model, we estimate $\ensuremath{\theta}$ to be 0.3730.3730.373, which is markedly distinct from its classical counterpart. Apart from the local order parameter, we also show that the entanglement entropy exhibits universal behavior in the short-time region. As the critical exponents in the early stage and in equilibrium are identical, we apply the short-time dynamics method to determine quantum critical properties. The method is generally applicable in both the Landau-Ginzburg-Wilson paradigm and topological phase transitions.
Recent work has suggested that the Kibble-Zurek mechanism can be re-interpreted as a theory of critical scaling out of equilibrium. While this has been shown for some classical and integrable models, in this work we demonstrate one crucial aspect of critical scaling theory: universality. We solve for the time-dependent finite-size scaling functions of the 1D transversefield Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally-studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and show that they should be robustly observable within present cold atom experiments. In addition, we discuss recent results in which the Ising model is extended by imbuing the magnetic field with dynamics. We predict using Kibble-Zurek scaling and numerically confirm that the magnetic field ramp is dynamically arrested at the quantum critical point. Extensions of this theory indicate that dynamic localization near critical points should be omnipresent in nature, and may have implications in particle physics as a possible mechanism for giving the Higgs boson a light mass.