Fixed points of Wegner-Wilson flows and many-body localization

Quantifying Unitary Flow Efficiency and Entanglement for Many-Body Localization

We probe the bulk geometry of the Wegner Wilson Flow (WWF) in the context of many-body localization, by addressing efficiency and bulk entanglement growth measures through approximating upper bounds on the boundary entanglement entropy. We connect these upper bounds to the Fubini-Study metric and clarify how a central quantity, the information fluctuation complexity, distinguishes bulk unitary rotation from entanglement production. We also give a short new proof of the small incremental entangling theorem in the absence of ancillas, achieving a dimension-independent, universal factor of $c= 2$…

Existence of a Phase with Finite Localization Length in the Double Scaling Limit of N-Orbital Models

Among the models of disordered conduction and localization, models with $N$ orbitals per site are attractive both for their mathematical tractability and for their physical realization in coupled disordered grains. However Wegner proved that there is no Anderson transition and no localized phase in the $N \rightarrow \infty$ limit, if the hopping constant $K$ is kept fixed. Here we show that the localized phase is preserved in a different limit where $N$ is taken to infinity and the hopping $K$ is simultaneously adjusted to keep $N \, K$ constant. We support this conclusion with two arguments.…

利用张量网络表示的连续幺正变换访问完整的多体局域化谱

Continuous unitary transformations using tensor network representations access the full many-body localized spectrum

本文提出变分连续幺正变换方法，结合Wegner-Wilson流方程与张量网络技术，用于近似对角化多体局域化哈密顿量，通过控制 bond 维度提升精度，并在 Heisenberg 链中验证了方法在不同系统规模下的有效性。

Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains

The iterative methods to diagonalize matrices and many-body Hamiltonians can be reformulated as flows of Hamiltonians towards diagonalization driven by unitary transformations that preserve the spectrum. After a comparative overview of the various types of discrete flows (Jacobi, QR-algorithm) and differential flows (Toda, Wegner, White) that have been introduced in the past, we focus on the random XXZ chain with random fields in order to determine the best closed flow within a given subspace of running Hamiltonians. For the special case of the free-fermion random XX chain with random fields, …

重整化群分析随机场XXZ链中的多体局域化相变

Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain

本文通过重整化群流分析随机场XXZ链的谱性质，发现其不支持单一参数标度形式或简单Wilson-Fisher固定点，而支持双参数Berezinskii-Kosterlitz-Thouless型流，揭示多体局域化相与局域化相变临界点的关系。

Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model

We consider the distribution function $P(|ψ|^{2})$ of the eigenfunction amplitude at the center-of-band (E=0) anomaly in the one-dimensional tight-binding chain with weak uncorrelated on-site disorder (the one-dimensional Anderson model). The special emphasis is on the probability of the anomalously localized states (ALS) with $|ψ|^{2}$ much larger than the inverse typical localization length $\ell_{0}$. Using the solution to the generating function $Φ_{an}(u,ϕ)$ found recently in our works we find the ALS probability distribution $P(|ψ|^{2})$ at $|ψ|^{2}\ell_{0} >> 1$. As an auxiliary prelimi…

格点量子色动力学中的局域化

Localization in Lattice QCD

本文研究了具有两种Wilson费米子的猝灭QCD的相图，提出了如下的微观图像。青木相内外的超临界区域的特征是存在密度接近零的（厄米）威尔逊-狄拉克算子模式，因此是一个非零的π凝聚。在青木相内，这种密度是由扩展的近零模式建立起来的，而在青木相外，有一个非零密度的指数局部近零模式，它发生在“例外”规范场配置。然而，没有戈德斯通激发出现以外的青木阶段，和戈德斯通激发的存在，因此可以用来定义青木阶段在淬火和未淬火的理论。我们发现，本地化的近零模式的密度引起一个发散的π介子两点函数，从而提供了一种替代机制，满足相关的沃德恒等式在存在一个非零的序参量。当我们把一个“扭曲”夸克质量取为零时，就会出现这种发散，我们得出结论，只有在扭曲质量不为零的情况下，具有威尔逊费米子的淬灭QCD才是定义良好的。我们表明，这种特殊的行为的近零模密度是特殊的淬火理论，通过证明这种密度消失在非淬火理论以外的青木阶段。我们讨论的影响畴壁和重叠费米子构造的威尔逊-狄拉克内核。我们认为，这两种方法的青木相外的工作，但失败的内部，因为局部性和/或手征对称性的问题，在淬火和未淬火的理论。