Fate of exceptional points under interactions: Reduction of topological classifications

TL;DR

This paper investigates how interactions affect the topological protection of exceptional points in non-Hermitian systems, revealing their fragility and classification reduction through topological invariants.

Contribution

It introduces a topological invariant framework for analyzing the impact of interactions on exceptional points and symmetry-protected rings in non-Hermitian topological classifications.

Findings

Exceptional points are fragile against interactions in 2D systems.

Topological invariants reveal the reduction of classifications due to interactions.

Results suggest similar phenomena may occur in broader non-Hermitian systems.

Abstract

Despite recent extensive studies of the non-Hermitian topology, understanding interaction effects is left as a crucial question. In this paper, we address interaction effects on exceptional points which are protected by the non-trivial point-gap topology unique to non-Hermitian systems. Our analysis in a two-dimensional parameter space elucidates the existence of exceptional points and symmetry-protected exceptional rings fragile against interactions; they are topologically protected only in non-interacting cases. This fragility of exceptional points and symmetry-protected exceptional rings arises from the reduction of non-Hermitian topological classifications, which is elucidated by introducing topological invariants of the second-quantized Hamiltonian for both non-interacting and interacting cases. These topological invariants are also available to analyze the reduction phenomena of gapped systems. The above results strongly suggest similar reduction phenomena of exceptional points in generic cases and open up a new direction of research in the non-Hermitian topology.