Floquet-engineered fidelity revivals in the PXP model

TL;DR

This work analyzes how a periodically driven PXP spin chain exhibits long-lived revival dynamics governed by the Floquet spectrum and the overlap structure with the initial state. Using Floquet theory, the authors identify Floquet spectrum narrowing (FSN) regions where revivals slow and propagate as a wave in driving-parameter space, with the dominant quasi-energy spacing Δε^F controlled by the Bessel factor J_0(h/ω_d). The Néel state shows robust, architecture-preserving revivals tied to an arc-like overlap with Floquet states, while interpolating initial states reveal hybrid, drive-tunable dynamics and multiple routes to avoid Floquet thermalization. These findings highlight a controllable mechanism to engineer and prolong non-ergodic dynamics, with potential implications for quantum information storage and tailored coherence in driven many-body systems, and suggest future work on alternative driving protocols and robustness of non-ergodic regimes. All mathematical notation is presented with proper Delimiters.

Abstract

We explore the dynamics of the PXP model when subjected to a periodic drive, and unveil the mechanism through which the interplay between spectral properties and initial states governs the emergence of dynamical revivals and their evolution across the space of driving parameters. For Néel-ordered initial states, revivals follow well-defined trajectories in the parameter space of the driving, primarily determined by a dominant quasi-energy spacing in the Floquet spectrum. Initial states interpolating between Néel and fully polarized configurations exhibit hybrid dynamics, which can be controlled by tuning their overlap with Floquet eigenstates via the driving parameters. This control also allows steering different routes for avoiding Floquet thermalization, showing how both initial state choice and driving protocol shape long-lived dynamics in this driven quantum many-body systems.

Figures (8)

• Figure 1: We consider a periodically driven quantum PXP model, schematically illustrated in the box at the top of the figure. When the system is initialized in the Néel state, the driving parameters control the revival dynamics, which follows a well-defined pathway. For other initial states, tuning the same driving parameters can give rise to alternative pathways, interpolating between qualitatively different dynamical regimes. Consequently, the system can access distinct dynamical regimes, as indicated by the blue arrow traversing different regions of the diagram.
• Figure 2: Panel (a): Floquet spectrum as a function of the driving amplitude $h$ with $\omega_d=5$ and $L=8$ fixed. The vertical dashed red lines indicate the first two zeros of the $J_0(h/\omega_d)$ Bessel function: $h/\omega_d \approx 2.4048,\, 5.5201$. Panel (b): one-period fidelity $\mathcal{F}(T)$ of the polarized $\ket{\boldsymbol{0}}$ (panel (b)) and the Nèel $\ket{\mathbb{Z}_2}$ (panel (c)) initial states as a function of both $h$ and $\omega_d$, with $L=12$. The red lines correspond to the zeros of $J_0(h/\omega_d)$. Panels (d),(e),(f),(g),(h),(i) report the fidelity between initial state (the system is initialized in the Nèel state) and time-evolved state at different stroboscopic times, labeled by $n$ on the top of each panel, with $L=12$. The evolution mechanism has the structure of a wave propagating in specific spatial regions identified by the zeros of the Bessel function. The spatial plane is fictitious and it is given by the driving parameters $h$ and $\omega_d$. We follow the crests of the evolving waves by the different red and orange symbols. Red symbols follow crests in the $h/\omega_d<2.4048$ region and orange symbols in the $2.4048<h/\omega_d<5.5201$.
• Figure 3: Spectral properties and dynamics of the $\ket{\mathbb{Z}_2}$ state in the regions of $h/\omega_d<2.4048$, i.e. the first zero of $J_0(h/\omega_d)$. Panels (a)-(d): deformation of the overlap between the Nèel state and the Floquet states for different values of the driving amplitude $h$, with $\omega_d=5$ and $L=12$. The four panels are associated to three specific regions of the driving amplitude $h$. Panels (e) and (f): revival time $n_{\rm rev}$ estimated from the Floquet spectrum as $n_{\rm rev}=\frac{T_{\rm rev}}{T}$ with $T_{\rm rev}=2\pi/\Delta\epsilon^F$, with $\Delta\epsilon^F$ extracted from the overlap between Nèel state and Floquet states, as a function of the driving amplitude $h$, normalized by the driving frequency $\omega_d$. In panel (e), we report it for different values of the size of the system $L$, with $\omega_d=5$. The inset contains the same object but zoomed in a specific region of $h$. Panel (f) reports the same quantity but for different values of $\omega_d$ and with $L=10$ fixed. Panels (h),(i) report the $n$-period fidelity $\mathcal{F}(nT)$ of the system initialized in the Nèel state as a function of $h$: panel (h) reports early times $n\leq 7$ and panel (i) reports later times $n\in [8,15]$. The red and blue arrows guide the eye along the time evolution of the revivals during the decay and revival phases, respectively. We consider $L=12$ and $\omega_d=5$.
• Figure 4: Revival mechanism in the region of $h/\omega_d$ in between the two zeros of $J_0(h/\omega_d)$: $2.4048<h/\omega_d < 5.5201$. We consider $\omega_d=5$ and $L=12$. Panel (a) shows the decay phase, where the fidelity monotonically decreases. Panel (b) shows the revival phase, where the fidelity grows in time following, in $h$, the trajectories indicated by the blue arrows. The blue arrow guides the eye along the time evolution of the revivals during the revival phase.
• Figure 5: Revival mechanism for the $\ket{\Theta_+}$ state with $\omega_d=5$ and $L=12$. Panel (a): overlap between the $\ket{\Theta_+}$ state and the Floquet eigenstates for different values of $\theta$ (different colors), computed at fixed $h = 5$. Panel (b): fidelity between the initial state $\ket{\Theta_+}$ and its stroboscopic time-evolved state at $t = 10T$, shown as a function of $h$ for several values of $\theta$ in the range $0$ to $\pi/2$. Panel (c): overlap between the $\ket{\Theta_+}$ state and the Floquet eigenstates for different values of $h$ (different colors), computed at fixed $\theta = \pi/4$. Panel (d): fidelity for $\theta = \pi/4$ evaluated at different stroboscopic times $nT$, with $n$ indicated in the legend. The blue arrow guides the eye along the time evolution of the revivals during the revival phase. In panels (a) and (c) the dashed black lines are guides to the eye highlighting the emergence of arc-like structures, while the dashed gray line indicates the corresponding arc structure for the Néel-state case.