Reduction of one-dimensional non-Hermitian point-gap topology by correlations

TL;DR

This paper investigates how correlations affect one-dimensional non-Hermitian topological systems, showing that interactions can reduce topological classifications and destroy phenomena like the skin effect, thus providing new insights into correlated non-Hermitian physics.

Contribution

It demonstrates that correlations reduce the topological classification from  to , and shows that interactions can eliminate the skin effect in one-dimensional non-Hermitian systems.

Findings

Correlations reduce the topological classification from  to .

Interactions destroy the skin effect in the extended Hatano-Nelson chain.

The fragility of the skin effect aligns with the reduction of point-gap topology.

Abstract

In spite of extensive works on the non-Hermitian topology, correlations effects remain crucial questions. We hereby analyze correlated non-Hermitian systems with special emphasis on the one-dimensional point-gap topology. Specifically, our analysis elucidates that correlations result in reduction of the topological classification $\mathbb{Z}\times \mathbb{Z} \to \mathbb{Z}$ for systems of one synthetic dimension with charge $\mathrm{U(1)}$ symmetry and spin-parity symmetry. Furthermore, we analyze an extended Hatano-Nelson chain which exhibits striking correlation effects; correlations destroy the skin effect at the non-interacting level. This fragility of the skin effect against interactions is consistent with the reduction of the point-gap topology in the one spatial dimension. The above discoveries shed new light on the topology of correlated systems and open up new directions of researches on non-Hermitian topological physics.