Non-Bloch Quantum Geometry of Non-Hermitian Systems

TL;DR

This paper develops a quantum geometric framework for non-Hermitian systems with open boundaries, linking real-space and non-Bloch band theories to characterize skin effects and localization.

Contribution

It introduces a unified quantum geometry approach for non-Hermitian systems, establishing an exact equivalence between real-space and non-Bloch quantum metrics.

Findings

Proves the equivalence between real-space and non-Bloch quantum metrics.

Defines localized non-Bloch Wannier functions in non-Hermitian systems.

Shows the non-Bloch quantum metric relates to Wannier function spread.

Abstract

We formulate quantum geometry for non-Hermitian systems under open boundary conditions. By defining quantum-geometric quantities in both real-space and non-Bloch representations, we establish a unified framework beyond conventional Bloch band theory. Our central result is an exact equivalence between the real-space integrated quantum metric and a non-Bloch integrated quantum metric defined on the generalized Brillouin zone. We further introduce localized non-Bloch Wannier functions in the presence of the non-Hermitian skin effect and show that the non-Bloch integrated quantum metric gives the gauge-invariant part of their spread functional. These results establish quantum geometry as a natural framework for characterizing open-boundary non-Hermitian band structures and the localization properties encoded in skin modes.