论文标题
寻找具有忠实易感性的非热门特殊点
Hunting for the non-Hermitian exceptional points with fidelity susceptibility
论文作者
论文摘要
在十年中，富达易感性已用于检测遗传性量子多体系统中的量子相变，在热力学限制下，保真度敏感性密度接近$+\ infty $。在这里，通过考虑希尔伯特空间的几何结构，将保真度的易感性$χ$推广到非热量子系统。我们选择了一个尺寸，而不是从头开始求解运动方程，而是选择了一个由生物双歧质特征组成的尺度，并且在不在特殊点（EP）上时可以通过代数或数字来解决。由于EP在Hilbert空间几何形状的特性，我们发现当$χ$接近$ - \ infty $时，可以找到EP。作为示例，我们调查了最简单的$ \ Mathcal {pt} $对称$ 2 \ times2 $ hamiltonian，带有单个调谐参数和非Hermitian Su-Schriffer-Heeger模型。
The fidelity susceptibility has been used to detect quantum phase transitions in the Hermitian quantum many-body systems over a decade, where the fidelity susceptibility density approaches $+\infty$ in the thermodynamic limits. Here the fidelity susceptibility $χ$ is generalized to non-Hermitian quantum systems by taking the geometric structure of the Hilbert space into consideration. Instead of solving the metric equation of motion from scratch, we chose a gauge where the fidelities are composed of biorthogonal eigenstates and can be worked out algebraically or numerically when not on the exceptional point (EP). Due to the properties of the Hilbert space geometry at EP, we found that EP can be found when $χ$ approaches $-\infty$. As examples, we investigate the simplest $\mathcal{PT}$ symmetric $2\times2$ Hamiltonian with a single tuning parameter and the non-Hermitian Su-Schriffer-Heeger model.
