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arXiv:1804.10226 · SciPost Physics Core

Out-of-equilibrium phase transitions induced by Floquet resonances in a periodically quench-driven XY spin chain

Sergio Enrique Tapias Arze, Pieter W. Claeys, Isaac Pérez Castillo, Jean-Sébastien Caux

Published Jul 22, 2020• 26 citations
arXivHTMLPDF

Abstract

We consider the dynamics of an XY spin chain subjected to an external transverse field which is periodically quenched between two values. By deriving an exact expression of the Floquet Hamiltonian for this out-of-equilibrium protocol with arbitrary driving frequencies, we show how, after an unfolding of the Floquet spectrum, the parameter space of the system is characterized by alternations between local and non-local regions, corresponding respectively to the absence and presence of Floquet resonances. The boundary lines between regions are obtained analytically from avoided crossings in the Floquet quasi-energies and are observable as phase transitions in the synchronized state. The transient behaviour of dynamical averages of local observables similarly undergoes a transition, showing either a rapid convergence towards the synchronized state in the local regime, or a rather slow one exhibiting persistent oscillations in the non-local regime, where explicit decay coefficients are presented.

DOI
10.21468/scipostphyscore.3.1.001

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We consider the dynamics of an XY spin chain subjected to an external transverse field which is periodically quenched between two values. By deriving an exact expression of the Floquet Hamiltonian for this out-of-equilibrium protocol with arbitrary driving frequencies, we show how, after an unfolding of the Floquet spectrum, the parameter space of the system is characterized by alternations between local and non-local regions, corresponding respectively to the absence and presence of Floquet resonances. The boundary lines between regions are obtained analytically from avoided crossings in the Floquet quasi-energies and are observable as phase transitions in the synchronized state. The transient behaviour of dynamical averages of local observables similarly undergoes a transition, showing either a rapid convergence towards the synchronized state in the local regime, or a rather slow one exhibiting persistent oscillations in the non-local regime, where explicit decay coefficients are presented.
We study the slow crossing of non-equilibrium quantum phase transitions in periodically driven systems. We explicitly consider a spin chain with a uniform time-dependent magnetic field and focus on the Floquet state that is adiabatically connected to the ground state of the static model. We find that this Floquet ground state undergoes a series of quantum phase transitions characterized by a non-trivial topology. To dynamically probe these transitions, we propose to start with a large driving frequency and slowly decrease it as a function of time. Combining analytical and numerical methods, we uncover a Kibble-Zurek scaling that persists in the presence of moderate interactions. This scaling can be used to experimentally demonstrate non-equilibrium transitions that cannot be otherwise observed.
We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.
We demonstrate that a boundary-localized periodic (Floquet) drive can induce nontrivial long-range correlations in a non-interacting fermionic chain which is additionally subject to boundary dissipation. Surprisingly, we find that this phenomenon occurs even when the corresponding isolated bulk is in a trivial gapped phase with exponentially decaying correlations. We argue that this boundary-drive induced non-equilibrium transition (as witnessed through the correlation matrix) is driven by a resonance mechanism whereby the drive frequency bridges bulk energy gaps, allowing boundary-injected particles and holes to propagate and mediate long-range correlations into the bulk. We also numerically establish that when the drive bridges a particle-hole gap, the induced long-range order scales as a power law with the bulk pairing potential (χ∼γ2χ\sim γ^2χ∼γ2). Our results highlight the potential of localized coherent driving for generating macroscopic order in open quantum systems.
Floquet dynamical quantum phase transitions (FDQPTs) reveal many nonequilibrium critical phenomena in periodically driven quantum systems, and their underlying mechanisms have attracted deep attention in recent years. In this paper, we consider an extended XY spin chain under a periodic flux-quench protocol, and demonstrate the effect of the flux difference within each micromotion period on the emergence of FDQPTs, by analyzing physical quantities such as the Loschmidt echo, rate function, and dynamical topological order parameter (DTOP), etc. We also generalize the concept of quench fidelity to periodically driven systems, i.e., Floquet quench fidelity, and discuss the necessary and sufficient conditions for FDQPTs. In contrast to conventional single-quench scenarios, the occurrence of FDQPTs is determined by the requirement of Floquet fidelity condition and segment duration. Our framework may be applied generally to arbitrary periodically driven parameters, providing fundamental insights into how periodic protocols control nonequilibrium phase transitions in quantum many-body systems.
Floquet theory is an indispensable tool for analyzing periodically driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviors of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution dynamics of the reservoir; and further explore how the driven system and the reservoir synchronize with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterized by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heat sink. At low frequencies, the driven system rapidly enters a synchronized state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we show that generic local-dissipation models that account for the influence of the reservoir on the driven system phenomenologically through Markovian dissipative equations of motion can generally not reproduce the rich behavior that our microscopic simulations reveal. In particular, such models prove insufficient to account for the suppression of overall energy absorption that is induced by the here observed synchronization between driven system and reservoir.
We study a generic class of fermionic two-band models under synchronized periodic driving, i.e., with the different terms in a Hamiltonian subject to periodic drives with the same frequency and phase. With all modes initially in a maximally mixed state, the synchronized drive is found to produce nonperiodic patterns of dynamical quantum phase transitions, with their appearance determined by an interplay of the band structure and the frequency of the drive. A case study of the anisotropic XY chain in a transverse magnetic field, transcribed to an effective two-band model, shows that the modes come with quantized geometric phases, allowing for the construction of an effective dynamical order parameter. Numerical studies in the limit of a strong magnetic field reveal distinct signals of precursors of dynamical quantum phase transitions also when the initial state of the XY chain is perturbed slightly away from maximal mixing, suggesting that the transitions may be accessible experimentally. A blueprint for an experiment built around laser-trapped circular Rydberg atoms is proposed.