Hunting for the non-Hermitian exceptional points with fidelity susceptibility

• URL: http://arxiv.org/abs/2009.07070v2
• Date: Thu, 17 Dec 2020 03:16:45 GMT
• Title: Hunting for the non-Hermitian exceptional points with fidelity susceptibility
• Authors: Yu-Chin Tzeng, Chia-Yi Ju, Guang-Yin Chen, Wen-Min Huang
• Abstract summary: The fidelity susceptibility has been used to detect quantum phase transitions in the Hermitian quantum many-body systems. Here the fidelity susceptibility $chi$ is generalized to non-Hermitian quantum systems by taking the geometric structure of the Hilbert space into consideration. As examples, we investigate the simplest $mathcalPT$ symmetric $2times2$ Hamiltonian with a single tuning parameter and the non-Hermitian Su-Schriffer-Heeger model.
• Score: 1.7205106391379026
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\chi$ 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 $\chi$ 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.

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