Local reminiscence in the PXP model

TL;DR

The study addresses how local memory can persist in a nonergodic, constrained quantum many-body system described by the PXP model. By analyzing local fidelities and reduced density matrices for several carefully chosen initial states, the authors uncover robust local reminiscence in the θ-symmetric Θ_+^{symm} state and the blockaded φ_L state, linking this behavior to the presence of scarred eigenstates in the pure-point spectrum. A spectral-measure framework shows that local reminiscence arises from the weight of the initial state on the scar subspace, while generic ergodic states exhibit vanishing long-time local memory due to an overwhelmingly absolutely continuous spectrum. These results highlight the coexistence of rich global dynamics with stable local memory and open avenues for understanding memory retention in constrained quantum systems and beyond.

Abstract

We study the emergence of local reminiscence in the PXP model, a constrained spin system realized in Rydberg atom arrays. The spectrum of this model is characterized by a majority of eigenstates that satisfy the eigenstate thermalization hypothesis, alongside a set of nonthermal eigenstates, known as quantum many-body scars, that violate it. While generic initial states lead to thermalization consistent with eigenstate thermalization hypothesis, special configurations generate non-ergodic dynamics and preserve memory of the initial state. In this work, we explore local memory retention using local fidelity and the dynamics of local observables. We find that two specific states, $θ$-symmetric and blockaded states, exhibit robust local reminiscence, with fidelities near unity and suppressed fluctuations as the system size increases. Our results show that non-ergodic regimes can sustain stable local memory while still allowing for complex global dynamics, providing new insights into quantum many-body scars and constrained dynamics.

Figures (6)

• Figure 1: Sketch of a local reminiscent dynamics: a system composed of $L$ qubits is initialized in the state $\ket{\psi(0)}$, whose $j$-site local density matrices $\rho_j(0)$ are obtained by tracing out the degrees of freedom of the rest of the chain from $\ket{\psi(0)}\bra{\psi(0)}$. The system undergoes a global time evolution governed by a Hamiltonian $H$, and this evolution is pictorially represented by a change in color of the global state. The system is locally reminiscent if local states, such as the time-evolved $j$-site local density matrices $\rho_j(t)$, are close to their counterparts at $t=0$.
• Figure 2: Global properties of the dynamics of the $\ket{\Theta_+}$ state. Panel (a): overlap of the state with the eigenstates of the Hamiltonian for $\theta=\pi/4$ and $L=20$. The states with larger overlap are highlighted in red. Panels (b),(c): dynamics of the global fidelity for $L=20$ and different values of $\theta$ (b) and for $\theta=\pi/4$ and different values of $L$. Panels (d),(e): dynamics of entanglement entropy for $L=20$ and different values of $\theta$ (d) and for $\theta=\pi/4$ and different values of $L$ (e), the inset reports the latter with entanglement entropy and times rescaled by $L$.
• Figure 3: Local properties of the dynamics of the $\ket{\Theta_+}$ state. Panel (a) and (b): dynamics of the single-site local fidelity averaged over the whole chain for $L=20$ and different $\theta$ (a), $\theta=\pi/4$ and different $L$(b). Panel (c): product of the all the single-site local fidelities for different values of $L$ and $\theta=\pi/4$. Panel (d): local fidelity evaluated on blocks $\mathcal{S}=[1,\ell]$ of different size with fixed $\theta=\pi/4$ and $L=20$. Panel (e): dynamics fluctuation of the $Z$-magnetization with respect to its initial value in each site for $L=20$ and $\theta=\pi/4$.
• Figure 4: Characterization of the $\theta$-symmetric state $\ket{\Theta_+^{\rm symm}}$ through its global and local features. Panels (a), (b) and (c) show the global features of the state, including the overlap with the eigenstates of the Hamiltonian for $L=20$ and $\theta=\pi/4$ (the states with larger overlap are highlighted in red) (a), the entanglement entropy and the global fidelity dynamics, respectively in panels (b) and (c), for $\theta=\pi/4$ and different $L$. In panel (b), the inset reports the dynamics of $S(t)$ for $\theta=\pi/4$ with both entanglement entropy and times rescaled by $L$. In panel (c), we compare the global fidelity with $\prod_{j=1}^L\mathcal{F}_j(t)$ for $L=20$ and $\theta=\pi/4$, which is reported in gray. Panels (d) and (e) show the dynamics of the local fidelity averaged over the whole chain, $\mathcal{F}_{1-\rm site}$. The dynamics is reported for $L=20$ and different values of $\theta$ (d), and for $\theta=\pi/4$ and different $L$ (e). Panels (f) and (g) show the time-average of the local fidelity $\mathcal{F}_{1-\rm site}$ and its associated standard deviation for $\theta=\pi/4$ and different $L$. Panel (h) shows dynamics fluctuation of the $Z$-magnetization with respect to its initial value in each site for $\theta=\pi/4$ and $L=20$.
• Figure 5: Characterization of the blockaded state $\ket{\varphi_L}$. Panels (a),(b),(c) and (d) report the global features of the states: overlap with the eigenstates with fixed $L=20$ (a), the state with larger overlap is the highest excited state $\ket{E_{n_{\rm max}}}$ and it is highlighted in red; in the inset we report the scaling of its entanglement entropy with the size $L$. Panel (b) reports the dynamics of the entanglement entropy and panel (c) the one of the global fidelity, panel (d) reports its time average. In panel (b), the inset reports the dynamics of $S(t)$ with both entanglement entropy and times rescaled by $L$. In panel (c), the global fidelity is compared with $\prod_j \mathcal{F}_j$ (gray line) for $L=20$. Panels (e),(g) and (h) report dynamics, time average and standard deviation of the local fidelity $\mathcal{F}_{1-\textrm{site}}$ for different $L$, panel (f) reports the fidelity over block of variable size with $L=20$. Panel (i) reports the dynamics of the fluctuation of the $Z$-magnetization with respect to its initial value in each site for $L=20$.