近日，华南师范大学的张丹伟及其研究小组与南京大学的Hai-Tao Ding合作并取得一项新进展。经过不懈努力，他们利用量子度规确认非厄米临界点。相关研究成果已于2024年11月5日在国际知名学术期刊《物理评论A》上发表。

在本文中，研究人员将这一智慧扩展到非厄米系统，以揭示非厄米临界点。具体而言，研究人员通过采用数值精确对角化和分析方法，计算了各种非厄米模型中的量子度规和相应的序参量，这些模型包括两个非厄米广义Aubry-André模型以及非厄米簇模型和混合场伊辛模型。

研究人员证明了这些非厄米模型中本征态的量子度规能够准确识别局域化转变、迁移率边以及伴随能隙闭合的多体量子相变。他们还进一步表明，这一策略对于有限尺寸效应和不同边界条件具有鲁棒性。

据悉，量子态的几何特性完全由量子几何张量编码。量子几何张量的实部和虚部分别为量子度规和贝里曲率，它们分别描述了希尔伯特空间中两个相邻量子态之间的距离和相位差。对于传统的厄米量子系统，量子度规对应于保真度敏感度，并且已经从几何角度被用于确定量子相变。

附：英文原文

Title: Identifying non-Hermitian critical points with the quantum metric

Author: Jun-Feng Ren, Jing Li, Hai-Tao Ding, Dan-Wei Zhang

Issue&Volume: 2024/11/05

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

DOI: 10.1103/PhysRevA.110.052203

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.052203