Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry

TL;DR

This paper investigates how chiral-inversion symmetry in a one-dimensional non-Hermitian system restores the bulk-boundary correspondence disrupted by the non-Hermitian Aharonov-Bohm effect, providing new insights into non-Hermitian topological phases.

Contribution

It introduces a symmetry-based approach to recover bulk-boundary correspondence in non-Hermitian systems, highlighting the role of chiral-inversion symmetry in topological phase transitions.

Findings

Chiral-inversion symmetry prevents nonzero imaginary magnetic flux.

Restoration of bulk-boundary correspondence with symmetric non-Hermiticity.

Topological invariant defined by vorticity of topological defects.

Abstract

Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological phase transition. However, the way of non-Hermiticity appearance may alter the system topology. By alternatively introducing the non-Hermiticity under symmetry to prevent nonzero imaginary magnetic flux, the bulk-boundary correspondence recovers and every bulk state becomes extended; the bulk topology of Bloch Hamiltonian predicts the (non)existence of edge states and topological phase transition. These are elucidated in a non-Hermitian Su-Schrieffer-Heeger model, where chiral-inversion symmetry ensures the vanishing of imaginary magnetic flux. The average value of Pauli matrices under the eigenstate of chiral-inversion symmetric Bloch Hamiltonian defines a vector field, the vorticity of topological defects in the vector field is a topological invariant. Our findings are applicable in other non-Hermitian systems. We first uncover the roles played by non-Hermitian AB effect and chiral-inversion symmetry for the breakdown and recovery of bulk-boundary correspondence, and develop new insights for understanding non-Hermitian topological phases of matter.