论文标题
在非热系统的特殊点附近的线性级别排斥
Linear level repulsions near exceptional points of non-Hermitian systems
论文作者
论文摘要
最接近的邻居间距分布是无序系统和通用的基本数量。众所周知，随机Hermitian系统的扩展和局部状态分别遵循Wigner-dyson和毒药分布，而Ginibre分布描述了具有复杂特征值的随机非热式系统。但是，仍然未知的是，具有全复杂特征值的Hermitian和非Hermitian的系统的水平分布尚不清楚。在这里，我们在非高汉顿人的特殊点附近展示了一系列新的普遍分布。需要两个通用分布函数，$ p _ {\ text {sp}}（s）$用于对称保存的阶段，而对称性 - 折叠阶段的$ p _ {\ p _ {\ text {sb}}（s）$对于对称性折叠阶段需要描述最近的邻居级级别间距分布。令人惊讶的是，与小$ s $的$ p _ {\ text {sp}}（s）$和$ p _ {\ text {sb}}（s）$相比，小$ s $与$ s $成正比，或与线性级别的排斥相比，与ginibre emembles的立方体排斥相反。对于非血症混乱的紧密结合汉密尔顿人，$ p _ {\ text {sp}}（s）$和$ p _ {\ text {sb}}}（s）$可以很好地描述$ p _ {\ text {sp（sb）}}（s）= \ tilde {c} _1s \ exp [ - \ tilde { - \ tilde {c} _2s^{\tildeα}] $在无限制的限制（无限型系统）中，其定位属于定位的定位，在无限型系统的热力学极限（无限型系统）中。
The nearest-neighbor level-spacing distributions are a fundamental quantity of disordered systems and universal. It is well-known that extended and localized states of random Hermitian systems follow the Wigner-Dyson and the Poison distributions, respectively, while the Ginibre distributions describe random non-Hermitian systems with complex eigenvalues. However, the level distribution of systems of neither Hermitian nor non-Hermitian with full complex eigenvalues is still unknown. Here we show a new class of universal level distributions in the vicinity of exceptional points of non-Hermitian Hamiltonians. Two universal distribution functions, $P_{\text{SP}}(s)$ for the symmetry-preserved phase and $P_{\text{SB}}(s)$ for the symmetry-broken phase, are needed to describe the nearest-neighbor level-spacing distributions near exceptional points. Surprisingly, both $P_{\text{SP}}(s)$ and $P_{\text{SB}}(s)$ are proportional to $s$ for small $s$, or a linear level repulsion, in contrast to the cubic level repulsions of the Ginibre ensembles. For non-Hermitian disordered tight-binding Hamiltonians, $P_{\text{SP}}(s)$ and $P_{\text{SB}}(s)$ can be well described by $P_{\text{SP(SB)}}(s)=\tilde{c}_1s\exp[-\tilde{c}_2s^{\tildeα}]$ in the thermodynamic limit (of infinite systems) with a constant $\tildeα$ that depends on the localization nature of states at exceptional points.
