New exact eigenstates in the Lesanovsky model, proximity to integrability and the PXP model, and approximate scar states

TL;DR

This paper explores the Lesanovsky Rydberg atom model, discovering new eigenstates, analyzing its proximity to integrability, and investigating potential many-body scar states related to the PXP model.

Contribution

It identifies two new exact low-lying eigenstates and proposes approximate scar states, advancing understanding of non-thermal eigenstates in Rydberg models.

Findings

Discovery of two new exact low-lying eigenstates.

Analysis of the model's proximity to integrability at small parameter z.

Proposals for approximate scar states in the Lesanovsky model.

Abstract

We study a model of Rydberg atoms in a nearest-neighbor Rydberg blockaded regime, introduced by Lesanovsky in Phys. Rev. Lett. 108, 105301 (2012). This many-body model (which has one parameter $z$) has an exactly known gapped liquid ground state, and two exactly known low-lying excitations. We discover two new exact low-lying eigenstates. We also discuss behavior of the model at small parameter $z$ and its proximity to an integrable model. Lastly, we discuss connections between the Lesanovsky model at intermediate $z$ and so-called PXP model. The PXP model describes a recent experiment that observed unusual revivals from a charge density wave initial state, which are attributed to a set of many-body "scar states" which do not obey the eigenstate thermalization hypothesis. We discuss the possibility of scar states in the Lesanovsky model and present two approximations for them.