标题： 二维非厄米哈塔诺-尼尔森通量模型中的反铁磁性和自旋激发 显示英文标题

标题： Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model

摘要： 一维Hatano-Nelson模型具有非互易跃迁，是相对简单的非厄米量子系统的一个显著例子，它允许研究开放量子系统中的各种现象，而无需添加额外的增益和损耗项。 在这里我们建议将其用作构建二维相关非厄米哈密顿量的基本单元。 它具有通量模型的特征形式，在每个plaquette（面元）上具有顺时针和逆时针方向的非互易跃迁。 通过添加位点上的Hubbard型相互作用，我们分析了长程反铁磁有序及其自旋激发的形成。 这种模型是非厄米的，但具有$\mathcal{PT}$对称性，这导致了两个区域的存在：未破缺$\mathcal{PT}$对称性的区域（实值谱）和破缺$\mathcal{PT}$对称性的区域（具有例外线和复值能谱）。 从一个区域到另一个区域的转变由位点相互作用参数的值控制，并与金属-绝缘体转变相一致。 我们还分析了自旋波谱，该谱由两种扩散型d波模式组成，分别对应于增益和损耗。 显示英文摘要

摘要： The one-dimensional Hatano-Nelson model with non-reciprocal hoppings is a prominent example of a relatively simple non-Hermitian quantum-mechanical system, which allows to study various phenomena in open quantum systems without adding extra gain and loss terms. Here we propose to use it as a building block to construct a correlated non-Hermitian Hamiltonian in two dimensions. It has the characteristic form of a flux model with clock-anticlockwise non-reciprocal hopping on each plaquette. Adding the on-site Hubbard type interaction we analyze the formation of the longe-range antiferromagnetic order and its spin excitations. Such a model is non-Hermitian, but $\mathcal{PT}$-symmetric, which leads to the existence of two regions: a region of unbroken $\mathcal{PT}$ symmetry (real-valued spectrum) and a region of broken $\mathcal{PT}$ symmetry with exceptional lines and complex-valued energy spectrum. The transition from one region to another is controlled by the value of the on-site interaction parameter and coincides with the metal-insulator transition. We also analyze the spin wave spectrum, which is characterized by two diffusive d-wave type of modes corresponding to gain and loss.