Non-Abelian Gauge Effect for 2-D Non-Hermitian Hatano-Nelson Model in Cylinder Type

TL;DR

This paper explores how non-Abelian gauge fields influence the topological and skin effect phenomena in a 2D non-Hermitian Hatano-Nelson model, revealing new topological states and localization behaviors.

Contribution

It introduces a novel polarization parameter from the generalized Brillouin zone to distinguish skin modes and demonstrates the unique impact of non-Abelian gauge on non-Hermitian topology.

Findings

Discovery of Hopf-link bulk braiding topology in the complex energy spectrum.

Introduction of a polarization parameter to identify skin modes.

Observation of zero-imaginary-energy eigenstates with degeneracy and bipolar localization.

Abstract

Non-Abelian gauge offers a powerful route to engineer novel topological phenomena. Here, we systematically investigate a two-dimensional (2D) non-Hermitian Hatano-Nelson model incorporating SU(2) non-Abelian gauge, demonstrating the emergence of Hopf-link bulk braiding topology in the complex energy spectrum solely with x-direction nearest-neighbor couplings. Because of the limitations of exceptional point (EP) topology in fully capturing the rich non-Hermitian skin effect (NHSE) under non-Abelian influence, we introduce a novel polarization parameter derived from the generalized Brillouin zone (GBZ). This parameter quantitatively discerns left-, right-, and notably, bipolar skin modes, with its accuracy corroborated by directly encoding real-space eigenstate. Our findings reveal that non-Abelian gauge provides unprecedented influence over NHSE, compared with Abelian gauge and without gauge cases. Furthermore, we uncover unique characteristics of zero-imaginary-energy eigenstates at these topological boundaries, including pronounced degeneracy and bipolar localization which is unaffected by size effects, investigated via dynamical evolution and Inverse Participation Ratio (IPR). This work establishes a new paradigm for synthesizing and manipulating non-Hermitian topological phases driven by non-Abelian structures, opening avenues for topological engineering and holding promise for experimental realization in synthetic dimensional platforms.