In this work we investigate the effects of configurational disorder on the eigenstates and dynamical properties of a tight-binding model on a quasi-one-dimensional comb lattice, consisting of a backbone decorated with linear offshoots of randomly distributed lengths. We show that all eigenstates are exponentially localized along the backbone of the comb. Moreover, we demonstrate the presence of an extensive number of compact localized states with precisely zero localization length. We provide an analytical understanding of these states and show that they survive in the presence of density-density interactions along the backbone of the system where, for sufficiently low but finite particle densities, they form many-body scar states. Finally, we discuss the implications of these compact localized states on the dynamical properties of systems with configurational disorder, and the corresponding appearance of long-lived transient behavior in the time evolution of physically relevant product states.

中文翻译：

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从紧凑的局部状态到随机量子梳中的多体疤痕

在这项工作中，我们研究了结构无序对准一维梳状晶格上的紧密结合模型的本征态和动力学性质的影响，准一维梳状晶格由装饰有随机分布长度的线性分支的主干组成。我们显示所有本征态都沿梳状骨干呈指数分布。此外，我们证明了存在大量的精确局部化长度为零的紧凑局部化状态。我们提供了对这些状态的分析理解，并表明它们在存在沿着系统主干的密度-密度相互作用的情况下生存，对于足够低但有限的粒子密度，它们会形成多体疤痕状态。最后，