Topology of multipartite non-Hermitian one-dimensional systems

TL;DR

This paper investigates the topology of multipartite non-Hermitian 1D systems, revealing novel phases characterized by complex-energy loops around exceptional points, with implications for understanding non-Hermitian topological phenomena.

Contribution

It introduces a detailed topological analysis of multipartite non-Hermitian systems, including a complete phase diagram and the connection between exceptional points and band topology.

Findings

Identification of composite cyclic loops encircling exceptional points

Topological characterization similar to Möbius strips and Penrose triangles

Analytical derivation of the phase diagram and phase boundaries

Abstract

The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts. These phases are characterized by composite cyclic loops of multiple complex-energy bands encircling single or multiple exceptional points (EPs) on the parametric space of real and imaginary energy. We show the topology of these composite loops is similar to well-known topological objects like M\"obius strips and Penrose triangles, and can be quantified by a nonadiabatic cyclic geometric phase which includes contributions only from the participating bands. We analytically derive a complete phase diagram with the phase boundaries of the model. We further examine the connection between the encircling of multiple EPs by complex-energy bands on parametric space and associated topology.