论文标题
整数特征多项式分解和希尔伯特空间碎片
Integer characteristic polynomial factorization and Hilbert space fragmentation
论文作者
论文摘要
具有希尔伯特空间碎片的模型的特征是（指数）许多动态断开的子空间，与常规对称性无关，而是由非平凡的Krylov子空间捕获。这些子空间通常表现出从混乱到整合到量子多体疤痕的整个热化特性。但是，到目前为止，鉴于哈密顿量，它们尚未得到适当的定义，也无法轻易找到它们。在这项工作中，我们考虑具有整数表示的哈密顿人，这是许多（大多数）浓缩物质中许多（大多数）著名模型的共同特征。我们显示了整数特征多项式分解的等效性以及由整数向量产生的Krylov子空间的存在。考虑到配对模型，我们说明了如何将分解属性用作揭示希尔伯特空间碎片的方法。我们讨论了对整数环的概括，例如基于环形磁场的概括，这些循环磁场在给定的（$ \ ne 0，π$）动量扇区时很重要。
Models with Hilbert space fragmentation are characterized by (exponentially) many dynamically disconnected subspaces, not associated with conventional symmetries but captured by nontrivial Krylov subspaces. These subspaces usually exhibit a whole range of thermalization properties, from chaotic to integrable, to quantum many-body scars. However, so far, they have not been properly defined, nor can they be easily found, given a Hamiltonian. In this work, we consider Hamiltonians that have integer representations, a common feature of many (most) celebrated models in condensed matter. We show the equivalence of the integer characteristic polynomial factorization and the existence of Krylov subspaces generated from integer vectors. Considering the pair-hopping model, we illustrate how the factorization property can be used as a method to unveil Hilbert space fragmentation. We discuss the generalization over other rings of integers, for example those based on the cyclotomic field which are relevant when working in a given ($\ne 0, π$) momentum sector.
