Unconventional early-time relaxation in the Rydberg chain

TL;DR

The paper shows that quantum many-body scars imprint a non-generic early-time relaxation in the survival probability (SP) of scarred initial states, with the decay rate set by the scar energy scale and overlaps rather than generic thermal broadening. By analyzing both perfect and approximate QMBS, notably in the PXP model for Rydberg chains, it demonstrates that the local density of states (LDOS) of scarred states is highly structured and scar-dominated, providing a measurable early-time signature that precedes, and is distinct from, long-time revivals. Using forward-scattering approximations and controlled deformations that either enhance revivals or restore ergodicity, the work quantifies how the SP decay rate encodes scar content, and presents a semiphenomenological LDOS model to generalize the condition under which scars dominate. The results offer practical guidance for detecting QMBS via early-time SP decay in current quantum simulators, with explicit time scales and experimental requirements highlighted for the Rydberg-PXP platform.

Abstract

We show that unconventional relaxation dynamics of special initial states in one-dimensional arrays of Rydberg atoms produce non-generic decay of the initial-state survival probability (SP) at very early times. Using the PXP hamiltonian as a minimal model of the Rydberg blockade, we prove that the early-time SP for states exhibiting quantum many-body scarring (QMBS) decays at a characteristic rate, whose finite-size scaling is determined solely by scars. We numerically investigate the effects of both revival-enhancing and ergodicity-restoring deformations of the PXP hamiltonian and find results consistent with the limiting cases of integrable and ergodic dynamics, respectively. We moreover argue that such unconventional early relaxation of scarred initial states is characteristic of a whole class of QMBS models. Since the SP can be easily measured experimentally, our findings enable us to probe the presence of scars at time scales much shorter than that of thermalization.

Figures (2)

• Figure 1: LDOS of the $\ket{\mathbb{Z}_2}$ state over the energy eigenbasis of PXP model with $J=1$ (\ref{['fig:LDOSpxpXZ']}) with revival-enhancing deformation ($g_{\text{PXPZ}}=0.048$), (\ref{['fig:LDOSpxp']}) without deformation, and (\ref{['fig:LDOSpxpNNN']}) with ergodicity-restoring deformation ($g_{\text{NNN}}=1$). The black dashed line is a Gaussian fit for the LDOS. All plots are obtained by Lanczos exact diagonalization for $L=28$ qubits with 400 iterations (histogrammed with 130 bins).
• Figure 2: FSA scars variance vs LDOS variance rescaled with system size as a function of deformation strength, for $L=24,\, 26,\, 28$ sites and $J=1$. (Right half) Variance when PXP is strongly deformed toward restoration of ergodicity. (Left half) Variance when PXP is perturbed toward perfect scarring behavior. The bare PXP model is at $g_{\text{PXPZ}}=g_{\text{NNN}}=0$. Black dashed lines are polynomial fit for a fixed system size $L=28$. Full LDOS data are obtained from regular Lanczos method with 400 iterations.