Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions

TL;DR

This paper investigates how quantum geometry behaves near non-Hermitian topological phase transitions, revealing diverse scaling laws and universality classes, including anomalous correlations and behaviors at exceptional points.

Contribution

It uncovers new scaling behaviors of quantum geometry in non-Hermitian systems, extending understanding of topological phase transitions and universality classes.

Findings

Different long-range couplings lead to distinct universality classes.

Quantum geometric tensor exhibits unique scaling near exceptional points.

Anomalous spatial behaviors in Wannier state correlations are observed.

Abstract

The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold close to different topological phase transitions in a non-Hermitian long-range extension of the Kitaev chain. The derivative of the geometric phase, as well as its scaling behavior, shows that systems with different long-range couplings can belong to distinct universality classes. Near certain criticalities, we further find that the Wannier state correlation function associated with extended Berry connection of the ground state exhibits spatially anomalous behaviors. Finally, we analyze the scaling of the quantum geometric tensor near phase transitions across exceptional points, shedding light on the emergence of novel universality classes.