General properties of fidelity in non-Hermitian quantum systems with PT symmetry

• URL: http://arxiv.org/abs/2203.01834v3
• Date: Tue, 21 Mar 2023 06:50:56 GMT
• Title: General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Authors: Yi-Ting Tu, Iksu Jang, Po-Yao Chang, Yu-Chin Tzeng
• Abstract summary: fidelity susceptibility is a tool for studying quantum phase transitions in the Hermitian condensed matter systems. We show that the fidelity $mathcalF$ is always real for the PT-unbroken states. We also study the two-legged non-Hermitian Su-Schrieffer-Heeger (SSH) model and the non-Hermitian XXZ spin chain.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The fidelity susceptibility is a tool for studying quantum phase transitions in the Hermitian condensed matter systems. Recently, it has been generalized with the biorthogonal basis for the non-Hermitian quantum systems. From the general perturbation description with the constraint of parity-time (PT) symmetry, we show that the fidelity $\mathcal{F}$ is always real for the PT-unbroken states. For the PT-broken states, the real part of the fidelity susceptibility $\mathrm{Re}[\mathcal{X}_F]$ is corresponding to considering both the PT partner states, and the negative infinity is explored by the perturbation theory when the parameter approaches the exceptional point (EP). Moreover, at the second-order EP, we prove that the real part of the fidelity between PT-unbroken and PT-broken states is $\mathrm{Re}\mathcal{F}=\frac{1}{2}$. Based on these general properties, we study the two-legged non-Hermitian Su-Schrieffer-Heeger (SSH) model and the non-Hermitian XXZ spin chain. We find that for both interacting and non-interacting systems, the real part of fidelity susceptibility density goes to negative infinity when the parameter approaches the EP, and verifies it is a second-order EP by $\mathrm{Re}\mathcal{F}=\frac{1}{2}$.

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