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Annalen der Physik

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

Hadi Cheraghi, S. Mahdavifar

Published Mar 29, 2021• 9 citations
Publisher

Abstract

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.

DOI
10.1002/andp.202000542

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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.
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 investigate the nonequilibrium quench dynamics of the one-dimensional transverse-field Ising model in both integrable and nonintegrable regimes. In particular, we report on a novel type of dynamical quantum phase transition (DQPT) that is characterized by a singular multipartite entanglement signature occurring at critical times in the post-quench dynamics. We show that this behavior is fundamentally distinct from previously studied DQPTs characterized by a nonanalytic rate function. We quantify the multipartite entanglement of the state by the quantum Fisher information and demonstrate that the DQPT belongs to a different universality class than the ground-state phase transition. Furthermore, we perform a spectral analysis of the DQPT and demonstrate that it is a genuine nonequilibrium transition arising from the constructive interference of excited states of the system during the many-body dynamics. Finally, we discuss potential experimental realizations in Rydberg platforms as well as applications in the context of quantum metrology.
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.
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.
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.
Quantum phase transition occurs at a quantum critical value of a control parameter such as the magnetic field in the Ising model in a transverse magnetic field (ITF). Recently, it is shown that ramping across the quantum critical point generates non-analytic behaviors in the time evolution of a closed quantum system in the thermodynamic limit at zero temperature. The mentioned phenomenon is called the dynamical quantum phase transition (DQPT). Here, we consider the one-dimensional ITF model with added the Dzyaloshinskii-Moriya interaction (DMI). Using the fermionization technique, the Hamiltonian is exactly diagonalized. Although the DMI induces chiral phase in the ground state phase diagram of the model, the study of the rate function of the return probability has proven that the DMI does not affect the DQPT. We conclude accordingly that the ramping across the quantum critical point is not a necessary and sufficient condition for DQPT.