We study a model of Rydberg atoms in a nearest-neighbor Rydberg blockaded regime, introduced by Lesanovsky [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 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 the 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 approximate scar states in the Lesanovsky model and present two approximations for them.

中文翻译：

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Lesanovsky模型中的精确本征态，接近可积性和PXP模型的近似本征状态

我们研究了由莱萨诺夫斯基[ Phys。牧师 108，105301（2012）]。这个多体模型（具有一个参数$ž$）具有完全已知的带隙液体基态和两个完全已知的低洼激发。我们发现了两个确切的低地本征态。我们还将讨论小参数情况下模型的行为$ž$以及它与可积模型的接近度。最后，我们讨论中间的Lesanovsky模型之间的联系$ž$以及所谓的PXP模型。PXP模型描述了一个最近的实验，该实验观察到了电荷密度波初始状态的异常恢复，这归因于一组不遵循本征态热化假设的多体“疤痕状态”。我们讨论了Lesanovsky模型中近似疤痕状态的可能性，并为它们提供了两种近似值。