论文标题
通过快速有效的构造方法，跨多体定位过渡的局部运动积分的结构特性
Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
论文作者
论文摘要
多体定位（MBL）是由于无序相互作用的量子系统中局部运动积分（LIOM）的出现而导致的恐怖性破坏的新型原型。为了更好地了解这种宏观上的lioms的作用，我们探索并研究了整个MBL过渡的某些结构特性。我们首先，考虑在无序磁场中的一维XXZ自旋链，并引入和实施一种非扰动，快速且准确的构建LIOM的方法。与已经存在的方法相反，我们的方案不仅允许在深MBL阶段获得LIOM，而且还可以在过渡点附近获得LIOM。然后，我们将liom运算符的矩阵表示为有向图的邻接矩阵，其元素描述了希尔伯特空间中有序的eigenbasis的连通性。我们对此图的群集大小分析表明，MBL过渡与希尔伯特空间中的渗透过渡一致。通过执行有限尺寸的缩放，我们比较了在存在和不存在相互作用的情况下，比较了关键障碍和相关指数$ν$。最后，我们还讨论了典型集群中Liom运算符的对角线元素的分布信号。
Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such macroscopically LIOMs, we explore and study some of their structural properties across the MBL transition. We first, consider a one-dimensional XXZ spin chain in a disordered magnetic field and introduce and implement a non-perturbative, fast, and accurate method of constructing LIOMs. In contrast to already existing methods, our scheme allows obtaining LIOMs not only in the deep MBL phase but rather, near the transition point too. Then, we take the matrix representation of LIOM operators as an adjacency matrix of a directed graph whose elements describe the connectivity of ordered eigenbasis in the Hilbert-space. Our cluster size analysis for this graph shows that the MBL transition coincides with a percolation transition in the Hilbert-space. By performing finite-size scaling, we compare the critical disorder and correlation exponent $ν$ both in the presence and absence of interaction. Finally, we also discuss how the distribution of diagonal elements of LIOM operators in a typical cluster signals the transition.
