Identifying non-Hermitian critical points with quantum metric

TL;DR

This paper extends the use of quantum geometric tensor analysis to non-Hermitian systems, demonstrating that the quantum metric can identify various critical points such as localization transitions and phase transitions, with robustness against finite-size effects.

Contribution

It introduces a method to detect non-Hermitian critical points using quantum metric, applying it to multiple models with numerical and analytical techniques, revealing new insights into non-Hermitian phase transitions.

Findings

Quantum metric identifies localization transitions.

Quantum metric detects mobility edges.

Quantum metric reveals non-Hermitian phase transitions.

Abstract

The geometric properties of quantum states is 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 work, 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-Andre 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.