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:1506.00477 · Physical Review B

Quenches and dynamical phase transitions in a nonintegrable quantum Ising model

Shraddha Sharma, Sei Suzuki, Amit Dutta

Published Sep 29, 2015• 117 citations
arXivHTMLPDF

Abstract

We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagnetic interactions in the presence of a longitudinal field which renders the model nonintegrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field. Analyzing the temporal evolution of the Loschmidt overlap, we find different possibilities of the presence (or absence) of dynamical phase transitions (DPTs) manifested in the nonanalyticities of the rate function of the return probability. Even though the model is nonintegrable, there are periodic occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic version of the model; this numerical finding is qualitatively explained by mapping the original model to an effective integrable spin model which is appropriate for describing such slow quenches. Furthermore, concerning the sudden quenches, our numerical results show that in some cases, DPTs can be present even when the spin chain is quenched within the same phase or even to the QCP, while in some other situations they completely disappear even after quenching across the QCP. These observations lead us to the conclusion that it is the change in the nature of the ground state that determines the presence of DPTs following a sudden quench.

DOI
10.1103/physrevb.92.104306

Related papers

Slow quenches in a quantum Ising chain: Dynamical phase transitions and topology

Shraddha Sharma, Uma Divakaran, Anatoli Polkovnikov +1 more

We study the slow quenching dynamics (characterized by an inverse rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian. Studying the Fisher zeros of the corresponding generalized ``partition function,'' we probe nonanalyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting ``lobe'' structure of Fisher zeros emerge. We have also made a connection to topological aspects studying the dynamical topological order parameter $[{\ensuremath{\nu}}_{D}(t)]$ as a function of time $(t)$ measured from the instant when the quenching is complete. Remarkably, the time evolution of ${\ensuremath{\nu}}_{D}(t)$ exhibits drastically different behavior following quenches across a single QCP and two QCPs. In the former case, ${\ensuremath{\nu}}_{D}(t)$ increases stepwise by unity at every DPT (i.e., $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{D}=1$). In the latter case, on the other hand, ${\ensuremath{\nu}}_{D}(t)$ essentially oscillates between 0 and 1 (i.e., successive DPTs occur with $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{D}=1$ and $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{D}=\ensuremath{-}1$, respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of the same sign.

arXiv:1601.01637•Physical review. B./Physical review. B•Apr 28, 2016•137 citations

Dynamical quantum phase transitions in the axial next-nearest-neighbor Ising chain

Johannes N. Kriel, Christoph Karrasch, Stefan K. Kehrein

We investigate sudden quenches across the critical point in the transverse field Ising chain with a perturbing nonintegrable next-nearest-neighbor interaction. Expressions for the return (Loschmidt) amplitude and associated rate function are derived to linear order in the next-nearest-neighbor coupling. In the thermodynamic limit these quantities exhibit nonanalytic behavior at a set of critical times, a phenomenon referred to as a dynamical quantum phase transition. We quantify the effect of the integrability breaking perturbation on the location and shape of these nonanalyticities. Our results agree with those of earlier numerical studies and offer further support for the assertion that the dynamical quantum phase transitions exhibited by this model are a generic feature of its postquench dynamics and are robust with respect to the inclusion of nonintegrable perturbations.

arXiv:1407.4036•Physical Review B•Sep 3, 2014•101 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

Tuning the presence of dynamical phase transitions in a generalized XY spin chain

Uma Divakaran, Shraddha Sharma, Amit Dutta

We study an integrable spin chain with three spin interactions and the staggered field $(\ensuremath{\lambda})$ while the latter is quenched either slowly [in a linear fashion in time $(t)$ as $t/\ensuremath{\tau}$, where $t$ goes from a large negative value to a large positive value and $\ensuremath{\tau}$ is the inverse rate of quenching] or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist nonanalyticities [known as dynamical phase transitions (DPTs)] in the subsequent real-time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when $\ensuremath{\tau}$ exceeds a critical value ${\ensuremath{\tau}}_{1})$, we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term $(\ensuremath{\gamma})$ and $\ensuremath{\tau}$, thereby establishing the existence of boundaries in the $(\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\tau})$ plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value ${\ensuremath{\lambda}}_{i}$ to a final value ${\ensuremath{\lambda}}_{f}$, we show that the condition for the presence of DPTs is governed by relations involving ${\ensuremath{\lambda}}_{i},{\ensuremath{\lambda}}_{f}$, and $\ensuremath{\gamma}$, and the spin chain must be swept across $\ensuremath{\lambda}=0$ for DPTs to occur.

arXiv:1601.04851•Physical review. E•May 18, 2016•63 citations

Dynamical Quantum Phase Transitions in the 1D Nonintegrable Spin‐1/2 Transverse Field XZZ Model

Hadi Cheraghi, S. Mahdavifar

Abstract Using the Jordan–Wigner mean‐field (JW‐MF) approach, the dynamical quantum phase transition (DQPT) in the 1D spin‐1/2 XZZ model is studied, where the presence of the transverse magnetic field breaks the U(1) symmetry of the Hamiltonian and leads to loss of integrability. In the time evolution of the rate function, three kinds of behaviors will emerge: regular and irregular nonanalytic, and also regular analytic. Examples are given where the rate function shows the regular analytic can appear albeit a quench is crossed from a quantum critical point (QCP) and examples where the irregular nonanalyticity behaviors can arise in both quenching into the same phase and exceeded from a QCP. All the regular nonanalyticity behaviors at periodic instants happen when quenches cross from a QCP. In order to achieve a confirmation on our results, the long‐time average of the rate function is determined and show the occurrence of the nonequilibrium quantum phase transitions exactly at the QCPs and hence disclose the JW‐MF approach qualitatively works very well.

Annalen der Physik•Mar 29, 2021•9 citations

Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions

Jad C. Halimeh, Maarten Van Damme, Lingzhen Guo +2 more

In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body physics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform matrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. Anomalous cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations in the antiferromagnetic case, showing that long-range interactions are not a sufficient condition for their appearance. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, regular cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups and we outline the associated experimental considerations.

arXiv:2106.05282•Physical review. B./Physical review. B•Sep 20, 2021•29 citations
We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagnetic interactions in the presence of a longitudinal field which renders the model nonintegrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field. Analyzing the temporal evolution of the Loschmidt overlap, we find different possibilities of the presence (or absence) of dynamical phase transitions (DPTs) manifested in the nonanalyticities of the rate function of the return probability. Even though the model is nonintegrable, there are periodic occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic version of the model; this numerical finding is qualitatively explained by mapping the original model to an effective integrable spin model which is appropriate for describing such slow quenches. Furthermore, concerning the sudden quenches, our numerical results show that in some cases, DPTs can be present even when the spin chain is quenched within the same phase or even to the QCP, while in some other situations they completely disappear even after quenching across the QCP. These observations lead us to the conclusion that it is the change in the nature of the ground state that determines the presence of DPTs following a sudden quench.
We study the slow quenching dynamics (characterized by an inverse rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian. Studying the Fisher zeros of the corresponding generalized ``partition function,'' we probe nonanalyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting ``lobe'' structure of Fisher zeros emerge. We have also made a connection to topological aspects studying the dynamical topological order parameter $[{\ensuremath{\nu}}_{D}(t)]$ as a function of time (t)(t)(t) measured from the instant when the quenching is complete. Remarkably, the time evolution of ${\ensuremath{\nu}}_{D}(t)$ exhibits drastically different behavior following quenches across a single QCP and two QCPs. In the former case, ${\ensuremath{\nu}}_{D}(t)$ increases stepwise by unity at every DPT (i.e., $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{D}=1$). In the latter case, on the other hand, ${\ensuremath{\nu}}_{D}(t)$ essentially oscillates between 0 and 1 (i.e., successive DPTs occur with $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{D}=1$ and $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{D}=\ensuremath{-}1$, respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of the same sign.
We investigate sudden quenches across the critical point in the transverse field Ising chain with a perturbing nonintegrable next-nearest-neighbor interaction. Expressions for the return (Loschmidt) amplitude and associated rate function are derived to linear order in the next-nearest-neighbor coupling. In the thermodynamic limit these quantities exhibit nonanalytic behavior at a set of critical times, a phenomenon referred to as a dynamical quantum phase transition. We quantify the effect of the integrability breaking perturbation on the location and shape of these nonanalyticities. Our results agree with those of earlier numerical studies and offer further support for the assertion that the dynamical quantum phase transitions exhibited by this model are a generic feature of its postquench dynamics and are robust with respect to the inclusion of nonintegrable perturbations.
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.
We study an integrable spin chain with three spin interactions and the staggered field $(\ensuremath{\lambda})$ while the latter is quenched either slowly [in a linear fashion in time (t)(t)(t) as $t/\ensuremath{\tau}$, where ttt goes from a large negative value to a large positive value and $\ensuremath{\tau}$ is the inverse rate of quenching] or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist nonanalyticities [known as dynamical phase transitions (DPTs)] in the subsequent real-time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when $\ensuremath{\tau}$ exceeds a critical value ${\ensuremath{\tau}}_{1})$, we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term $(\ensuremath{\gamma})$ and $\ensuremath{\tau}$, thereby establishing the existence of boundaries in the $(\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\tau})$ plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value ${\ensuremath{\lambda}}_{i}$ to a final value ${\ensuremath{\lambda}}_{f}$, we show that the condition for the presence of DPTs is governed by relations involving ${\ensuremath{\lambda}}_{i},{\ensuremath{\lambda}}_{f}$, and $\ensuremath{\gamma}$, and the spin chain must be swept across $\ensuremath{\lambda}=0$ for DPTs to occur.
Abstract Using the Jordan–Wigner mean‐field (JW‐MF) approach, the dynamical quantum phase transition (DQPT) in the 1D spin‐1/2 XZZ model is studied, where the presence of the transverse magnetic field breaks the U(1) symmetry of the Hamiltonian and leads to loss of integrability. In the time evolution of the rate function, three kinds of behaviors will emerge: regular and irregular nonanalytic, and also regular analytic. Examples are given where the rate function shows the regular analytic can appear albeit a quench is crossed from a quantum critical point (QCP) and examples where the irregular nonanalyticity behaviors can arise in both quenching into the same phase and exceeded from a QCP. All the regular nonanalyticity behaviors at periodic instants happen when quenches cross from a QCP. In order to achieve a confirmation on our results, the long‐time average of the rate function is determined and show the occurrence of the nonequilibrium quantum phase transitions exactly at the QCPs and hence disclose the JW‐MF approach qualitatively works very well.
In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body physics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform matrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. Anomalous cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations in the antiferromagnetic case, showing that long-range interactions are not a sufficient condition for their appearance. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, regular cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups and we outline the associated experimental considerations.