Identifying non-Hermitian critical points with quantum metric

• DOI: 10.48550/arxiv.2404.15628
• Publication Date: 2024-04-23
• Authors: Jun-Feng Ren; Jing Li; Hai-Tao Ding; Dan-Wei Zhang
• Keywords: Quantum Physics; FOS: Physical sciences; Quantum Physics (quant-ph)

The geometric properties of quantum states is fully encoded by the tensor. real and imaginary parts tensor are metric Berry curvature, which characterize distance phase difference between two nearby in Hilbert space, respectively. For conventional Hermitian systems, corresponds to fidelity susceptibility has already been used specify transitions from perspective. In this work, we extend wisdom non-Hermitian systems for revealing critical points. To be concrete, employing numerical exact diagonalization analytical methods, calculate corresponding order parameters various models, include generalized Aubry-Andr\'{e} models cluster mixed-field Ising models. We demonstrate that eigenstates these exactly identifies localization transitions, mobility edges, many-body further show strategy robust against finite-size effect different boundary conditions.