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:2211.14256 · Physical review. B./Physical review. B

Dynamical quantum phase transition without an order parameter

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

Published Mar 8, 2023• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.107.094304

Related papers

Scaling and Universality at Dynamical Quantum Phase Transitions

Markus Heyl

Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.

arXiv:1505.02352•Physical Review Letters•Oct 2, 2015•242 citations

Finite-component dynamical quantum phase transitions

Ricardo Puebla

Phase transitions have recently been formulated in the time domain of quantum many-body systems, a phenomenon dubbed dynamical quantum phase transitions (DPTs), whose phenomenology is often divided in two types. One refers to distinct phases according to long-time averaged order parameters, while the other is focused on the nonanalytical behavior emerging in the rate function of the Loschmidt echo. Here we show that such DPTs can be found in systems with few degrees of freedom; i.e., they can take place without resorting to the traditional thermodynamic limit. We illustrate this by showing the existence of the two types of DPTs in a quantum Rabi model---a system involving a spin-$\frac{1}{2}$ and a bosonic mode. The dynamical criticality appears in the limit of an infinitely large ratio of the spin frequency with respect to the bosonic one. We determine its dynamical phase diagram and study the long-time averaged order parameters, whose semiclassical approximation yields a jump at the transition point. We find the critical times at which the rate function becomes nonanalytical, showing its associated critical exponent as well as the corrections introduced by a finite frequency ratio. Our results open the door for the study of DPTs without the need to scale up the number of components, thus allowing for their investigation in well controllable systems.

arXiv:2008.13762•Physical review. B./Physical review. B•Dec 10, 2020•40 citations

Quenching a quantum critical state by the order parameter: Dynamical quantum phase transitions and quantum speed limits

Markus Heyl

The dynamics in the vicinity of quantum phase transitions entails a variety of important and universal phenomena, such as critical slowing down or the Kibble-Zurek mechanism, which are associated with the low-energy and long-time properties at criticality. Here, the author reveals that the opposite regime of transient nonequilibrium time evolution at criticality can similarly host universal temporal behavior. By strongly perturbing a quantum critical state through quenching the associated order parameter, the system experiences a dynamical quantum phase transition with physical quantities becoming nonanalytic at critical times. These dynamical quantum phase transitions are caused by superextensive energy fluctuations induced by the particular protocol, which turn out to have profound consequences for quantum speed limits and potential restricted thermalization despite the nonintegrability of the system.

arXiv:1608.06659•Physical review. B./Physical review. B•Feb 9, 2017•69 citations

Dynamical phase transitions after quenches in nonintegrable models

Christoph Karrasch, Dirk Schuricht

We investigate the dynamics following sudden quenches across quantum critical points belonging to different universality classes. Specifically, we use matrix product state methods to study the quantum Ising chain in the presence of two additional terms which break integrability. We find that in all models the rate function for the return probability to the initial state becomes a nonanalytic function of time in the thermodynamic limit. This so-called ``dynamical phase transition'' was first observed in a recent work by Heyl, Polkovnikov, and Kehrein [Phys. Rev. Lett. 110, 135704 (2013)] for the exactly-solvable quantum Ising chain, which can be mapped to free fermions. Our results for ``interacting theories'' indicate that nonanalytic dynamics is a generic feature of sudden quenches across quantum critical points. We discuss potential connections to the dynamics of the order parameter.

arXiv:1302.3893•Physical Review B•May 3, 2013•246 citations

Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model

Markus Heyl, Anatoli Polkovnikov, Stefan K. Kehrein

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.

arXiv:1206.2505•Physical Review Letters•Mar 28, 2013•860 citations

Anomalous correlation-induced dynamical phase transitions

Niaz Ali Khan, Pei Wang, Munsif Jan +1 more

The nonanalyticity of the Loschmidt echo at critical times in quantum quenched systems is termed as the dynamical quantum phase transition, extending the notion of quantum criticality to a nonequilibrium scenario. In this paper, we establish a new paradigm of dynamical phase transitions driven by a sudden change in the internal spatial correlations of the disorder potential in a low-dimensional disordered system. The quench dynamics between prequenched pure and postquenched random system Hamiltonian reveals an anomalous dynamical quantum phase transition triggered by an infinite disorder correlation in the modulation potential. The physical origin of the anomalous phenomenon is associated with the overlap between the two distinctly different extended states. Furthermore, we explore the quench dynamics between the prequenched random and postquenched pure system Hamiltonian. Interestingly, the quenched system undergoes dynamical quantum phase transitions for the prequench white-noise potential in the thermodynamic limit. In addition, the quench dynamics also shows a clear signature of the delocalization phase transition in the correlated Anderson model.

arXiv:2302.08206•Scientific Reports•Jun 10, 2023•21 citations
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.
Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.
Phase transitions have recently been formulated in the time domain of quantum many-body systems, a phenomenon dubbed dynamical quantum phase transitions (DPTs), whose phenomenology is often divided in two types. One refers to distinct phases according to long-time averaged order parameters, while the other is focused on the nonanalytical behavior emerging in the rate function of the Loschmidt echo. Here we show that such DPTs can be found in systems with few degrees of freedom; i.e., they can take place without resorting to the traditional thermodynamic limit. We illustrate this by showing the existence of the two types of DPTs in a quantum Rabi model---a system involving a spin-12\frac{1}{2}21​ and a bosonic mode. The dynamical criticality appears in the limit of an infinitely large ratio of the spin frequency with respect to the bosonic one. We determine its dynamical phase diagram and study the long-time averaged order parameters, whose semiclassical approximation yields a jump at the transition point. We find the critical times at which the rate function becomes nonanalytical, showing its associated critical exponent as well as the corrections introduced by a finite frequency ratio. Our results open the door for the study of DPTs without the need to scale up the number of components, thus allowing for their investigation in well controllable systems.
The dynamics in the vicinity of quantum phase transitions entails a variety of important and universal phenomena, such as critical slowing down or the Kibble-Zurek mechanism, which are associated with the low-energy and long-time properties at criticality. Here, the author reveals that the opposite regime of transient nonequilibrium time evolution at criticality can similarly host universal temporal behavior. By strongly perturbing a quantum critical state through quenching the associated order parameter, the system experiences a dynamical quantum phase transition with physical quantities becoming nonanalytic at critical times. These dynamical quantum phase transitions are caused by superextensive energy fluctuations induced by the particular protocol, which turn out to have profound consequences for quantum speed limits and potential restricted thermalization despite the nonintegrability of the system.
We investigate the dynamics following sudden quenches across quantum critical points belonging to different universality classes. Specifically, we use matrix product state methods to study the quantum Ising chain in the presence of two additional terms which break integrability. We find that in all models the rate function for the return probability to the initial state becomes a nonanalytic function of time in the thermodynamic limit. This so-called ``dynamical phase transition'' was first observed in a recent work by Heyl, Polkovnikov, and Kehrein [Phys. Rev. Lett. 110, 135704 (2013)] for the exactly-solvable quantum Ising chain, which can be mapped to free fermions. Our results for ``interacting theories'' indicate that nonanalytic dynamics is a generic feature of sudden quenches across quantum critical points. We discuss potential connections to the dynamics of the order parameter.
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.
The nonanalyticity of the Loschmidt echo at critical times in quantum quenched systems is termed as the dynamical quantum phase transition, extending the notion of quantum criticality to a nonequilibrium scenario. In this paper, we establish a new paradigm of dynamical phase transitions driven by a sudden change in the internal spatial correlations of the disorder potential in a low-dimensional disordered system. The quench dynamics between prequenched pure and postquenched random system Hamiltonian reveals an anomalous dynamical quantum phase transition triggered by an infinite disorder correlation in the modulation potential. The physical origin of the anomalous phenomenon is associated with the overlap between the two distinctly different extended states. Furthermore, we explore the quench dynamics between the prequenched random and postquenched pure system Hamiltonian. Interestingly, the quenched system undergoes dynamical quantum phase transitions for the prequench white-noise potential in the thermodynamic limit. In addition, the quench dynamics also shows a clear signature of the delocalization phase transition in the correlated Anderson model.