We present here the nonequilibrium dynamics of the recently studied quasiperiodic Ising model. The zero temperature phase diagram of this model mainly consists of three phases, where each of these three phases can have extended, localized, or critically delocalized low-energy excited states. We explore the nature of excitations in these different phases by studying the evolution of entanglement entropy after performing sudden quenches of different strengths to different phases. Our results on nonequilibrium dynamics of entanglement entropy are concurrent with the nature of excitations predicted in Chandran and Laumann [Phys. Rev. X 7, 031061 (2017)].
We present here the nonequilibrium dynamics of the recently studied quasiperiodic Ising model. The zero temperature phase diagram of this model mainly consists of three phases, where each of these three phases can have extended, localized, or critically delocalized low-energy excited states. We explore the nature of excitations in these different phases by studying the evolution of entanglement entropy after performing sudden quenches of different strengths to different phases. Our results on nonequilibrium dynamics of entanglement entropy are concurrent with the nature of excitations predicted in Chandran and Laumann [Phys. Rev. X 7, 031061 (2017)].
Much has been learned regarding dynamical quantum phase transition (DQPT) due to sudden quenches across quantum critical points in traditional quantum systems. However, not much has been explored when a system undergoes a localization-delocalization transition. Here, we study one-dimensional fermionic systems in presence of a quasiperiodic potential, which induces delocalization-localization transition even in one dimension. We show signatures of DQPT in the many-body dynamics, when quenching is performed between phases belonging to different universality classes. We investigate how the nonanalyticity in the dynamical free energy gets affected with filling fractions in the bare system and, further, study the fate of DQPT under interaction. Strikingly, whenever quenching is performed from the low-entangled localized phase to the high-entangled delocalized phase, our studies suggest an intimate relationship between DQPT and the rate of the entanglement growth: Faster growths of entanglement entropy ensures quicker manifestation of the nonanalyticities in the many-body dynamical free energy.
We study the non-equilibrium dynamics of a quasiperiodic quantum Ising chain after a sudden change in the strength of the transverse field at zero temperature. In particular, we consider the dynamics of the entanglement entropy and the relaxation of the magnetization. The entanglement entropy increases with time as a power law, and the magnetization is found to exhibit stretched-exponential relaxation. These behaviors are explained in terms of anomalously diffusing quasiparticles, which are studied in a wave packet approach. The non-equilibrium magnetization is shown to have a dynamical phase transition.
In this paper, we analytically study phase transitions in quasiperiodically driven one-dimensional quantum critical systems that are described by conformal field theories (CFTs). The phase diagrams and phase transitions can be analytically obtained by using Avila's global theory in one-frequency quasiperiodic cocycles. Compared to previous works where the quasiperiodicity was introduced in the driving time and no phase transitions were observed [Wen et al., Phys. Rev. Res. 3, 023044 (2021)], here we propose a setup where the quasiperiodicity is introduced in the driving Hamiltonians. In our setup, one can observe the heating phases, nonheating phases, and phase transitions. The phase diagram as well as the Lyapunov exponents that determine the entanglement entropy evolution can be analytically obtained. In addition, based on Avila's theory, we prove there is no phase transition in the previously proposed setup of quasiperiodically driven CFTs [Wen et al., Phys. Rev. Res. 3, 023044 (2021)]. We verify our field theory results by studying the time evolution of entanglement entropy on lattice models.
We study the dynamical quantum phase transitions (DQPTs) manifested in the subsequent unitary dynamics of an extended Ising model with an additional three spin interactions following a sudden quench. Revisiting the equilibrium phase diagram of the model, where different quantum phases are characterized by different winding numbers, we show that in some situations the winding number may not change across a gap closing point in the energy spectrum. Although, usually there exists a one-to-one correspondence between the change in winding number and the number of critical time scales associated with DQPTs, we show that the extended nature of interactions may lead to unusual situations. Importantly, we show that in the limit of the cluster Ising model, three critical modes associated with DQPTs become degenerate, thereby leading to a single critical time scale for a given sector of Fisher zeros.
We study the nonequilibrium dynamics of an isolated bipartite quantum system, the sunburst quantum Ising model, under interaction quench. The prequench limit of this model is two noninteracting integrable systems, namely a transverse Ising chain and finite number of isolated qubits. As a function of interaction strength, the spectral fluctuation property goes from Poisson to Wigner-Dyson statistics. We chose entanglement entropy as a probe to study the approach to thermalization or lack of it in postquench dynamics. In the near-integrable limit, as expected, the linear entropy displays oscillatory behavior, while in the chaotic limit it saturates. Along with the chaotic nature of the time evolution generator, we show the importance of the role played by the coherence of the initial state in deciding the nature of thermalization. We further show that these findings are general by replacing the Ising ring with a disordered XXZ model with disorder strength putting it in the many-body localized phase.
We study the dynamics and the resulting state after relaxation in a quasidisordered integrable lattice system after a sudden quench. Specifically, we consider hard-core bosons in an isolated one-dimensional geometry in the presence of a quasiperiodic potential whose strength is abruptly changed to take the system out of equilibrium. In the delocalized regime, we find that the relaxation dynamics of one-body observables, such as the density, the momentum distribution function, and the occupation of the natural orbitals, follow, to a good approximation, power laws. In that regime, we also show that the observables after relaxation can be described by the generalized Gibbs ensemble, while such a description fails for the momentum distribution and the natural orbital occupations in the presence of localization. At the critical point, the relaxation dynamics is found to be slower than in the delocalized phase.