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:1206.2505 · Physical Review Letters

Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model

Markus Heyl, Anatoli Polkovnikov, Stefan K. Kehrein

Published Mar 28, 2013• 860 citations
arXivHTMLPDF

Abstract

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to nonanalytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this Letter we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely nonanalytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse-field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.

DOI
10.1103/physrevlett.110.135704

Related papers

Disentangling dynamical phase transitions from equilibrium phase transitions

Szabolcs Vajna, Balázs Dóra

Dynamical phase transitions (DPTs) occur after quenching some global parameters in quantum systems, and are signalled by the nonanalytical time evolution of the dynamical free energy, which is calculated from the Loschmidt overlap between the initial and time evolved states. In a recent Letter [M. Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)], it was suggested that DPTs are closely related to equilibrium phase transitions (EPTs) for the transverse field Ising model. By studying a minimal model, the XY chain in a transverse magnetic field, we show analytically that this connection does not hold generally. We present examples where DPT occurs without crossing any equilibrium critical lines by the quench, and a nontrivial example with no DPT but crossing a critical line by the quench. Although the nonanalyticities of the dynamical free energy on the real time axis do not indicate the presence or absence of an EPT, the structure of Fisher lines for complex times reveals a qualitative difference.

arXiv:1401.2865•Physical Review B•Apr 7, 2014•223 citations

Quantum quench dynamics in the transverse field Ising model at nonzero temperatures

Nils O. Abeling, Stefan K. Kehrein

The recently discovered dynamical phase transition denotes nonanalytic behavior in the real-time evolution of quantum systems in the thermodynamic limit, and it has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this paper, we extend the analysis to nonzero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at nonzero temperatures still displays features derived from the zero-temperature nonanalyticities, it is shown that in this model dynamical phase transitions do not exist if $T>0$. This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free-energy density.

arXiv:1510.08728•Physical review. B./Physical review. B•Mar 11, 2016•84 citations

Quantum phase transitions far from equilibrium in short-range transverse field Ising models

Ceren B. Dağ, Kai Sun

Dynamical phase transitions (DPTs) are generally defined under two different but related categories: DPT-I where the equilibrium value, or long-time average, of the order parameter as a function of the control parameter demonstrates a phase boundary; DPT-II where the Loschmidt return rate shows a cusp singularity in real-time dynamics. Quenched from polarized states, one-point observables have featureless steady state regimes for short-range transverse field Ising models (TFIM), which prevents them from exhibiting DPT-I, unlike long-range TFIM. In this Letter, we incorporate Lieb-Robinson bounds into the definition of DPT by choosing appropriate temporal cutoffs and show that in the lightcone, a quantum phase transition (QPT) far from equilibrium could emerge with an associated scaling law at the vicinity of the transition. More specifically, the observable at the cutoff could exhibit order parameterlike behavior in analogy to equilibrium quantum criticality, however with certain important differences that we discuss in detail. The scaling of the dynamical order parameter at the vicinity is determined via the decay rate of the observable in time, hence rendering the QPT a truly nonequilibrium phase transition. We apply the procedure to both integrable and nonintegrable short-range TFIM and elaborate on how the QPT signature changes with integrability.

•Apr 26, 2020•0 citations

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

Johannes Lang, Bernhard Frank, Jad C. Halimeh

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of ${\mathbb{Z}}_{2}$ symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

arXiv:1712.02175•Physical review. B./Physical review. B•May 3, 2018•97 citations

Dynamical quantum phase transition without an order parameter

O. N. Kuliashov, A. A. Markov, Alexey N. Rubtsov

Short-time dynamics of many-body systems may exhibit nonanalytical behavior of the systems' properties at particular times, thus dubbed dynamical quantum phase transition. Simulations showed that in the presence of disorder, new critical times appear in the quench evolution of the Ising model. We study the physics behind these new critical times. We discuss the spectral features of the Ising model responsible for the disorder-induced phase transitions. We found the critical value of the disorder sufficient to induce the dynamical phase transition as a function of the number of spins. Most importantly, we argue that this dynamical phase transition while nontopological lacks a local order parameter.

arXiv:2211.14256•Physical review. B./Physical review. B•Mar 8, 2023•19 citations

Dynamical quantum phase transitions in the quantum Potts chain

Christoph Karrasch, Dirk Schuricht

The time evolution of a quantum system after a sudden change of one of its parameters may show characteristic nonanalyticities, provided that this quench crosses a quantum phase transition. The authors investigate the relation between such dynamical quantum phase transitions and the universal properties of the corresponding quantum critical point.

arXiv:1701.04214•Physical review. B./Physical review. B•Feb 23, 2017•58 citations
A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to nonanalytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this Letter we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely nonanalytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse-field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.
Dynamical phase transitions (DPTs) occur after quenching some global parameters in quantum systems, and are signalled by the nonanalytical time evolution of the dynamical free energy, which is calculated from the Loschmidt overlap between the initial and time evolved states. In a recent Letter [M. Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)], it was suggested that DPTs are closely related to equilibrium phase transitions (EPTs) for the transverse field Ising model. By studying a minimal model, the XY chain in a transverse magnetic field, we show analytically that this connection does not hold generally. We present examples where DPT occurs without crossing any equilibrium critical lines by the quench, and a nontrivial example with no DPT but crossing a critical line by the quench. Although the nonanalyticities of the dynamical free energy on the real time axis do not indicate the presence or absence of an EPT, the structure of Fisher lines for complex times reveals a qualitative difference.
The recently discovered dynamical phase transition denotes nonanalytic behavior in the real-time evolution of quantum systems in the thermodynamic limit, and it has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this paper, we extend the analysis to nonzero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at nonzero temperatures still displays features derived from the zero-temperature nonanalyticities, it is shown that in this model dynamical phase transitions do not exist if T>0T>0T>0. This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free-energy density.
Dynamical phase transitions (DPTs) are generally defined under two different but related categories: DPT-I where the equilibrium value, or long-time average, of the order parameter as a function of the control parameter demonstrates a phase boundary; DPT-II where the Loschmidt return rate shows a cusp singularity in real-time dynamics. Quenched from polarized states, one-point observables have featureless steady state regimes for short-range transverse field Ising models (TFIM), which prevents them from exhibiting DPT-I, unlike long-range TFIM. In this Letter, we incorporate Lieb-Robinson bounds into the definition of DPT by choosing appropriate temporal cutoffs and show that in the lightcone, a quantum phase transition (QPT) far from equilibrium could emerge with an associated scaling law at the vicinity of the transition. More specifically, the observable at the cutoff could exhibit order parameterlike behavior in analogy to equilibrium quantum criticality, however with certain important differences that we discuss in detail. The scaling of the dynamical order parameter at the vicinity is determined via the decay rate of the observable in time, hence rendering the QPT a truly nonequilibrium phase transition. We apply the procedure to both integrable and nonintegrable short-range TFIM and elaborate on how the QPT signature changes with integrability.
We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2{\mathbb{Z}}_{2}Z2​ symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.
Short-time dynamics of many-body systems may exhibit nonanalytical behavior of the systems' properties at particular times, thus dubbed dynamical quantum phase transition. Simulations showed that in the presence of disorder, new critical times appear in the quench evolution of the Ising model. We study the physics behind these new critical times. We discuss the spectral features of the Ising model responsible for the disorder-induced phase transitions. We found the critical value of the disorder sufficient to induce the dynamical phase transition as a function of the number of spins. Most importantly, we argue that this dynamical phase transition while nontopological lacks a local order parameter.