Periodically driven Rydberg chains with staggered detuning

Abstract

We study the stroboscopic dynamics of a periodically driven finite Rydberg chain with staggered ($\mathrm{\ensuremath{\Delta}}$) and time-dependent uniform $[\ensuremath{\lambda}(t)]$ detuning terms using exact diagonalization. We show that at intermediate drive frequencies (${\ensuremath{\omega}}_{D}$), the presence of a finite $\mathrm{\ensuremath{\Delta}}$ results in violation of the eigenstate thermalization hypothesis (ETH) via clustering of Floquet eigenstates. Such clustering is lost at special commensurate drive frequencies for which $\ensuremath{\hbar}{\ensuremath{\omega}}_{d}=n\mathrm{\ensuremath{\Delta}}$ ($n\ensuremath{\in}Z$) leading to restoration of ergodicity. The violation of ETH in these driven finite-sized chains is also evident from the dynamical freezing displayed by the density-density correlation between Rydberg excitations at even sites of the chain for specific ${\ensuremath{\omega}}_{D}$. Such a correlator exhibits stable oscillations with perfect revivals when driven close to the freezing frequencies for initial all spin-down ($|0\ensuremath{\rangle}$) or Neel ($|{\mathbb{Z}}_{2}\ensuremath{\rangle}$, with up spins on even sites) states. In contrast, for the $|{\overline{\mathbb{Z}}}_{2}\ensuremath{\rangle}$ (time-reversed partner of $|{\mathbb{Z}}_{2}\ensuremath{\rangle}$) initial state, we find complete absence of such oscillations leading to freezing for a range of ${\ensuremath{\omega}}_{D}$; this range increases with $\mathrm{\ensuremath{\Delta}}$. We also study the properties of quantum many-body scars in the Floquet spectrum of the model as a function of $\mathrm{\ensuremath{\Delta}}$ and show the existence of mid-spectrum scars at large $\mathrm{\ensuremath{\Delta}}$ which do not have overlap with either $|0\ensuremath{\rangle}$ or $|{\mathbb{Z}}_{2}\ensuremath{\rangle}$ states. We supplement our numerical results with those from an analytic Floquet Hamiltonian computed using Floquet perturbation theory which allows us to provide qualitative analytical explanations of the above-mentioned numerical results.

Topics & Concepts