Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice

TL;DR

This paper investigates the emergence of mobility rings and topological phase transitions in a non-Hermitian, non-Abelian quasiperiodic lattice, revealing new localization phenomena and exact analytical expressions.

Contribution

It introduces the concept of mobility rings in a non-Hermitian non-Abelian lattice and provides exact analytical expressions for their properties, advancing understanding of localization and topology.

Findings

Mobility rings separate localized and extended states in the complex energy plane.

Analytical expressions for mobility rings are derived and confirmed numerically.

Numerical indicators like participation ratio and winding number support the existence of mobility rings.

Abstract

We study localization and topological properties in spin-1/2 non-reciprocal Aubry-Andr\'{e} chain with SU(2) non-Abelian artificial gauge fields. The results reveal that, different from the Abelian case, mobility rings, will emerge in the non-Abelian case accompanied by the non-Hermitian topological phase transition. As the non-Hermitian extension of mobility edges, such mobility rings separate Anderson localized eigenstates from extended eigenstates in the complex energy plane under the periodic boundary condition. Based on the topological properties, we obtain the exact expression of the mobility rings. Furthermore, the corresponding indicators such as inverse participation rate, normalized participation ratio, winding number, non-Hermitian spectral structures and wave functions are numerically studied. The numerical results are in good agreement with the analytical expression, which confirms the emergence of mobility rings.