Winding-control mechanism of non-Hermitian systems

TL;DR

This paper introduces a winding-control mechanism for non-Hermitian quantum systems that manipulates spectral properties and boundary effects through conditional boundary conditions, enhancing understanding of non-Hermitian topology.

Contribution

It presents a novel winding-control mechanism using CBCs to selectively collapse spectra and reconstruct Brillouin zones, advancing non-Hermitian spectral and topological analysis.

Findings

Winding-control mechanism collapses PBC spectra onto OBC spectra based on winding numbers.

Eigenstates exhibit nontrivial skin effects and extended behaviors due to BZ and GBZ interplay.

Numerical demonstrations across various models deepen understanding of non-Hermitian physics.

Abstract

Non-Hermitian quantum systems exhibit various interesting and inter-connected spectral, topological, and boundary-sensitive features. By introducing conditional boundary conditions (CBCs) for non-Hermitian quantum systems, we explore a winding-control mechanism that selectively collapses specific periodic boundary condition (PBC) loop-type spectra onto their open boundary condition (OBC) counterparts, guided by their specific winding numbers, together with a composite reconstruction of the Brillouin zone (BZ) and generalized Brillouin zone (GBZ). The corresponding eigenstates also manifest nontrivial skin effects or extended behaviors arising from the interplay between BZ and GBZ structures. Intuitively, the winding-control mechanism is tied to the residual imaginary velocity originating from the corresponding Fermi sea, establishing the CBCs as the transition boundaries between different non-Hermitian topology of spectral windings. Furthermore, we can generalize our control by incorporating similarity transformations and holomorphic mappings with the boundary controls. We demonstrate the winding control numerically within various models, which enriches our knowledge of non-Hermitian physics across the spectrum, topology, and bulk-boundary correspondence.