非厄米XX自旋链的PT对称性：来自复边界场的非局域体相互作用

厄米矩阵模型的体普适性及其相关性质

Bulk Universality and Related Properties of Hermitian Matrix Models

在假定决定模型的势是全局$C^{2}$和局部$C^{3}$函数的条件下，给出了厄米矩阵模型谱块普适性的新证明（见定理\ref{t:U.t1}）.与我们之前在\cite{Pa-Sh:97}中的证明一样，该证明基于正交多项式技术，但不使用正交多项式的渐近性。相反，我们得到的$sin$ -内核作为一个独特的解决方案，一定的非线性积分微分方程，从行列式公式的关联函数的模型。本文还对关于本征值的极限归一化计数测度的存在性和性质的论文\cite{BPS:95}进行了简化和加强。我们使用这些结果的普遍性的证明，我们相信，他们是独立的利益。

A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators

We show how, given a non-Hermitian Hamiltonian $H$, we can generate new non-Hermitian operators sequentially, producing a virtually infinite chain of non-Hermitian Hamiltonians which are isospectral to $H$ and $H^\dagger$ and whose eigenvectors we can easily deduce in an almost automatic way; no ingredients are necessary other than $H$ and its eigensystem. To set off the chain and keep it running, we use, for the first time in our knowledge, a series of maps all connected to different metric operators. We show how the procedure works in several physically relevant systems. In particular, we ap…

Topological Classificaton of Non-Hermitian Gapless Phases: Exceptional Points and Bulk Fermi Arcs

We provide classification of gapless phases in non-Hermitian systems according to two types of complex-energy gaps: point gap and line gap. We show that exceptional points, at which not only eigenenergies but also eigenstates coalesce, are characterized by gap closing of point gaps with nontrivial topological charges. Moreover, we find that bulk Fermi arcs accompanying exceptional points are robust because of topological charges for real line gaps. On the basis of the classification, some examples are also discussed.

具有独立同分布元素的复非厄米特矩阵的体 universality

Bulk Universality for Complex non-Hermitian Matrices with Independent and Identically Distributed Entries

本文研究了复非厄米特矩阵的体 universality，证明了在元素独立同分布且具有有限矩的条件下，通过 Tao 和 Vu 的四矩定理可消除 Gaussian 扰动分量，并证明体相关函数在大 N 极限下是 universal 的。

Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems

The Nielsen-Ninomiya theorem is a fundamental theorem on the realization of chiral fermions in static lattice systems in high-energy and condensed matter physics. Here we extend the theorem in dynamical systems, which include the original Nielsen-Ninomiya theorem in the static limit. In contrast to the original theorem, which is a no-go theorem for bulk chiral fermions, the new theorem permits them due to bulk topology intrinsic to dynamical systems. The theorem is based on duality enabling a unified treatment of periodically driven systems and non-Hermitian ones. We also present the extended …

二维非厄米特系统中的体-边对应：Toeplitz算子与奇异值

Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values

该研究通过Toeplitz算子和奇异值建立了二维非厄米特系统中体-边对应关系，揭示了奇异值在拓扑保护中的关键作用，并展示了拓扑保护的边缘态和角落态。

Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain

A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to N=1024 spins) that our approach leads to a significant reduction of the annealing time that is proportional to $\ln N$, which is much less than the time (proportional to $N^2$) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms.

稀疏复非厄米随机矩阵的体相普适性

Bulk Universality for Sparse Complex non-Hermitian Random Matrices

本文证明具有独立元素且矩衰减条件满足的稀疏复非厄米随机矩阵，其体相局部特征值统计量具有普适性，主要工具为稀疏多预解式局部律。

边界耗散自旋链中的无标度非厄米趋肤效应

Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain

本文研究PT对称非厄米边界场下开放XXZ自旋链，通过坐标Bethe ansatz发现相互作用诱导的无标度非厄米趋肤效应，构造PT破缺相稳态与基态并给出热力学极限本征能量，探讨多体无标度态与边界弦态差异及各向同性点转变，并提出实验验证方案。

具有非厄米四次项的一维玻色紧束缚链中的守恒量

Conserved quantities in a bosonic tight-binding chain with non-Hermitian quartic terms

本文研究非厄米玻色子晶格中的局域守恒量，通过傅里叶变换和三角恒等式推导出相互对易的守恒量族，并扩展到多种相互作用形式，提供统一构造框架。

违反局部电荷的全或无图象的非厄米特玻色子链

Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains

研究展示了非厄米特玻色子链中存在k-local电荷的系统，推翻了局部交换电荷的全或无行为的普遍假设，并揭示了3-local电荷的Grabowski-Mathieu可积性测试不具普遍适用性。

点隙拓扑相中的体-边对应关系

Bulk-boundary correspondence in point-gap topological phases

本文建立了非厄米系统点隙拓扑中的体-边对应关系，揭示了开放边界与周期边界条件下体点隙拓扑的差异，并基于实空间拓扑不变量和K-理论给出完整分类，证明非平凡开放边界拓扑导致稳健且奇异的表面态。