Identifying non-Hermitian critical points with quantum metric

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.

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• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Recent progress on disorder-induced topological phases
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
• Probing phase transitions in non-Hermitian systems with quantum entanglement