多体局域化：通过块实空间重整化构造突现局部守恒算子
Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
摘要：
完全多体定域量子无序系统的特征是大量的局域守恒算符的出现，这些算符阻止了系统向热平衡弛豫。这些局域守恒算符可以看作是整个本征态的基石。在本文中，我们建议通过一些块实空间重整化显式地构造它们。其原理是，每个RG步骤对角化最小的剩余块，并为每个块产生一个守恒算子。$N$自旋链的最终输出是具有$\left(\frac{\ln N}{\ln 2}\right)$层的$N$保守算子的分层组织。顶层守恒算符的系统尺寸性质对于描述激发本征态的可能长程有序和不同FMBL相位之间可能的临界点是必要的。我们讨论的相似之处和差异，强无序RSRG-X方法，通过一个二叉树的$N$层生成的整个集合的$2^N$本征态。该方法被应用到长程量子自旋玻璃伊辛模型，其中所构建的激发本征态被发现是完全一样的基态在另一个无序实现，使他们可以在顺磁相，在自旋玻璃相或临界。
英文摘要：
A Fully Many-Body Localized (FMBL) quantum disordered system is characterized by the emergence of an extensive number of local conserved operators that prevents the relaxation towards thermal equilibrium. These local conserved operators can be seen as the building blocks of the whole set of eigenstates. In this paper, we propose to construct them explicitly via some block real-space renormalization. The principle is that each RG step diagonalizes the smallest remaining blocks and produces a conserved operator for each block. The final output for a chain of $N$ spins is a hierarchical organization of the $N$ conserved operators with $\left(\frac{\ln N}{\ln 2}\right)$ layers. The system-size nature of the conserved operators of the top layers is necessary to describe the possible long-ranged order of the excited eigenstates and the possible critical points between different FMBL phases. We discuss the similarities and the differences with the Strong Disorder RSRG-X method that generates the whole set of the $2^N$ eigenstates via a binary tree of $N$ layers. The approach is applied to the Long-Ranged Quantum Spin-Glass Ising model, where the constructed excited eigenstates are found to be exactly like ground states in another disorder realization, so that they can be either in the paramagnetic phase, in the spin-glass phase or critical.
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