论文标题
量子疤痕作为弱“破碎”谎言代数表示的嵌入
Quantum scars as embeddings of weakly "broken" Lie algebra representations
论文作者
论文摘要
我们提出了对疤痕状态和量子复兴的解释，即由多体量子系统的特征态的子集跨越的谎言代数的弱“破碎”表示。我们表明，描述了强烈相互互动的Rydberg原子的PXP模型支持多个$ \ Mathrm {su（2）} $的“松散”嵌入，该嵌入与对应于疤痕特征的不同家族的代数。此外，我们证明可以通过迭代过程逐渐使这些嵌入更加准确，从而导致最佳扰动，从而稳定了来自任意电荷密度波产物状态的复兴状态，$ | \ m m m mathbb {z} _n \ rangle $，包括在未经扰动的PXP模型中没有显示复活的$。我们讨论了PXP模型中存在的谎言代数的松散嵌入与相关模型中疤痕状态的最新构造之间的关系。
We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple $\mathrm{su(2)}$ Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, $|\mathbb{Z}_n\rangle$, including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models.
