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:0908.4590 · Physical Review B

Anomalous nonergodic scaling in adiabatic multicritical quantum quenches

Shusa Deng, Gerardo Ortíz, Lorenza Viola

Published Dec 30, 2009• 41 citations
arXivHTMLPDF

Abstract

We investigate nonequilibrium dynamical scaling in adiabatic quench processes across quantum multicritical points. Our analysis shows that the resulting power-law scaling depends sensitively on the control path and that anomalous critical exponents may emerge depending on the universality class. We argue that the observed anomalous behavior originates in the fact that the dynamical excitation process takes place asymmetrically with respect to the static multicritical point and that noncritical energy modes may play a dominant role. As a consequence, dynamical scaling requires introducing genuinely nonstatic exponents.

DOI
10.1103/physrevb.80.241109

Related papers

Dynamical critical scaling and effective thermalization in quantum quenches: Role of the initial state

Shusa Deng, Gerardo Ortíz, Lorenza Viola

We explore the robustness of universal dynamical scaling behavior in a quantum system near criticality with respect to initialization in a large class of states with finite energy. By focusing on a homogeneous $\mathit{XY}$ quantum spin chain in a transverse field, we characterize the nonequilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of the initial state. In particular, we identify conditions on the initial distribution of quasiparticle excitation that ensure that Kibble-Zurek scaling persists. The emergence of effective thermal equilibrium behavior following a sudden quench toward criticality is also investigated, with focus on the long-time expectation value of the quasiparticle number operator. Despite the integrability of the $\mathit{XY}$ model, this observable is found to behave thermally in quenches to a regular quantum critical point, provided that the system is initially prepared at sufficiently high temperature. However, a similar thermalization behavior fails to occur in quenches toward a multicritical point. We argue that the observed lack of thermalization originates in this case in the asymmetry of the impulse region that is also responsible for anomalous multicritical dynamical scaling.

arXiv:1011.0781•Physical Review B•Mar 25, 2011•38 citations

Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching

Victor Mukherjee, Amit Dutta

We study adiabatic quantum quenches across a quantum multicritical point (MCP) using a quenching scheme that enables the system to hit the MCP along different paths. We show that the power-law scaling of the defect density with the rate of driving depends non-trivially on the path, i.e. , the exponent varies continuously with the parameter α that defines the path, up to a critical value α=α c ; on the other hand for α⩾α c , the scaling exponent saturates to a constant value. We show that dynamically generated and path (α)- dependent effective critical exponents associated with the quasicritical points lying close to the MCP (on the ferromagnetic side), where the energy-gap is minimum, lead to this continuously varying exponent. The scaling relations are established using the integrable transverse XY spin chain and generalized to a MCP associated with a d -dimensional quantum many-body systems (not reducible to two-level systems) using adiabatic perturbation theory. We also calculate the effective path-dependent dimensional shift d 0 (α) (or the shift in center of the impulse region) that appears in the scaling relation for special paths lying entirely in the paramagnetic phase. The numerically obtained results are in good agreement with analytical predictions.

arXiv:1006.3343•Europhysics Letters (EPL)•Nov 1, 2010•39 citations

Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions

S. Deng, Gerardo Ortíz, Lorenza Viola

We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points ( i.e. , critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general non-trivially path-dependent, and detailed knowledge about the time-dependent excitation process becomes essential. In particular, we show how multiple level crossings within a gapless phase may completely suppress excitation depending on the control path. Our results typify non-ergodic scaling in continuous finite-order quantum phase transitions.

arXiv:0809.2831•Europhysics Letters (EPL)•Dec 1, 2008•119 citations

Dynamical relaxation behaviors of a critical quench

Yin-Tao Zou, Chengxiang Ding

We study the universal dynamical relaxation behaviors of a quantum XY chain following a quench, paying special attention to the case in which the initial state is a critical ground state, or the postquenched Hamiltonian is at a critical point of equilibrium quantum phase transition, or both of them are critical. In such a ``critical quench,'' we find very interesting real-time dynamical scaling behaviors and we find crossover phenomena between them. For a quench from a noncritical point to a critical point, we find that, compared to the noncritical quench, the universal power-law scaling behavior does not change; however, there may be a crossover between the exponential decaying behavior and the power-law scaling. For a quench from a critical point to a noncritical point, the power-law scaling behaviors ${t}^{\ensuremath{-}3/2}$ and ${t}^{\ensuremath{-}3/4}$ in the noncritical quenches may be changed to ${t}^{\ensuremath{-}1}$ and ${t}^{\ensuremath{-}1/2}$, respectively. If the prequenched Hamiltonian is set to be a point that is close to but not exactly at a critical point, we find interesting crossover phenomena between different power-law scaling behaviors. We also study the quench from the vicinity of a multicritical point, we find crossover behaviors that are induced by a different mechanism, and we find another crossover exponent. All the results are related to the gap-closing properties of the energy spectrum of the critical points.

arXiv:2305.00160•Physical review. B./Physical review. B•Jul 19, 2023•13 citations

Universal Postquench Prethermalization at a Quantum Critical Point

Pia Gagel, Peter P. Orth, Jörg Schmalian

We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive nonequilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are: (i) a power law rise of order and correlations after an initial collapse of the equilibrium state and (ii) a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.

arXiv:1406.6387•Physical Review Letters•Nov 26, 2014•54 citations

Quench dynamics near a quantum critical point

Claudia De Grandi, Vladimir Gritsev, Anatoli Polkovnikov

We study the dynamical response of a system to a sudden change of the tuning parameter $\ensuremath{\lambda}$ starting (or ending) at the quantum critical point. In particular, we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude, and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order $m$ at the quantum critical point, where $m$ is related to the power of the quench. Precisely for sudden quenches, the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite-temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold-atom experiments.

arXiv:0909.5181•Physical Review B•Jan 19, 2010•230 citations
We investigate nonequilibrium dynamical scaling in adiabatic quench processes across quantum multicritical points. Our analysis shows that the resulting power-law scaling depends sensitively on the control path and that anomalous critical exponents may emerge depending on the universality class. We argue that the observed anomalous behavior originates in the fact that the dynamical excitation process takes place asymmetrically with respect to the static multicritical point and that noncritical energy modes may play a dominant role. As a consequence, dynamical scaling requires introducing genuinely nonstatic exponents.
We explore the robustness of universal dynamical scaling behavior in a quantum system near criticality with respect to initialization in a large class of states with finite energy. By focusing on a homogeneous XY\mathit{XY}XY quantum spin chain in a transverse field, we characterize the nonequilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of the initial state. In particular, we identify conditions on the initial distribution of quasiparticle excitation that ensure that Kibble-Zurek scaling persists. The emergence of effective thermal equilibrium behavior following a sudden quench toward criticality is also investigated, with focus on the long-time expectation value of the quasiparticle number operator. Despite the integrability of the XY\mathit{XY}XY model, this observable is found to behave thermally in quenches to a regular quantum critical point, provided that the system is initially prepared at sufficiently high temperature. However, a similar thermalization behavior fails to occur in quenches toward a multicritical point. We argue that the observed lack of thermalization originates in this case in the asymmetry of the impulse region that is also responsible for anomalous multicritical dynamical scaling.
We study adiabatic quantum quenches across a quantum multicritical point (MCP) using a quenching scheme that enables the system to hit the MCP along different paths. We show that the power-law scaling of the defect density with the rate of driving depends non-trivially on the path, i.e. , the exponent varies continuously with the parameter α that defines the path, up to a critical value α=α c ; on the other hand for α⩾α c , the scaling exponent saturates to a constant value. We show that dynamically generated and path (α)- dependent effective critical exponents associated with the quasicritical points lying close to the MCP (on the ferromagnetic side), where the energy-gap is minimum, lead to this continuously varying exponent. The scaling relations are established using the integrable transverse XY spin chain and generalized to a MCP associated with a d -dimensional quantum many-body systems (not reducible to two-level systems) using adiabatic perturbation theory. We also calculate the effective path-dependent dimensional shift d 0 (α) (or the shift in center of the impulse region) that appears in the scaling relation for special paths lying entirely in the paramagnetic phase. The numerically obtained results are in good agreement with analytical predictions.
We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points ( i.e. , critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general non-trivially path-dependent, and detailed knowledge about the time-dependent excitation process becomes essential. In particular, we show how multiple level crossings within a gapless phase may completely suppress excitation depending on the control path. Our results typify non-ergodic scaling in continuous finite-order quantum phase transitions.
We study the universal dynamical relaxation behaviors of a quantum XY chain following a quench, paying special attention to the case in which the initial state is a critical ground state, or the postquenched Hamiltonian is at a critical point of equilibrium quantum phase transition, or both of them are critical. In such a ``critical quench,'' we find very interesting real-time dynamical scaling behaviors and we find crossover phenomena between them. For a quench from a noncritical point to a critical point, we find that, compared to the noncritical quench, the universal power-law scaling behavior does not change; however, there may be a crossover between the exponential decaying behavior and the power-law scaling. For a quench from a critical point to a noncritical point, the power-law scaling behaviors ${t}^{\ensuremath{-}3/2}$ and ${t}^{\ensuremath{-}3/4}$ in the noncritical quenches may be changed to ${t}^{\ensuremath{-}1}$ and ${t}^{\ensuremath{-}1/2}$, respectively. If the prequenched Hamiltonian is set to be a point that is close to but not exactly at a critical point, we find interesting crossover phenomena between different power-law scaling behaviors. We also study the quench from the vicinity of a multicritical point, we find crossover behaviors that are induced by a different mechanism, and we find another crossover exponent. All the results are related to the gap-closing properties of the energy spectrum of the critical points.
We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive nonequilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are: (i) a power law rise of order and correlations after an initial collapse of the equilibrium state and (ii) a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.
We study the dynamical response of a system to a sudden change of the tuning parameter $\ensuremath{\lambda}$ starting (or ending) at the quantum critical point. In particular, we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude, and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order mmm at the quantum critical point, where mmm is related to the power of the quench. Precisely for sudden quenches, the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite-temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold-atom experiments.