An intrinsic topological model in the absence of symmetry

TL;DR

This paper explores a classical ring's vibrational spectrum, revealing topologically nontrivial bands and fractional boundary states driven by exceptional points, without relying on symmetry.

Contribution

It introduces a topological model based on exceptional points in a classical system lacking symmetry, expanding topological physics understanding.

Findings

Identification of fractional boundary states in a classical system

Topologically protected fractional exceptional points in bulk

Topological nontrivial bands without symmetry constraints

Abstract

We study the vibrational spectrum of a constrained classical ring. Due to the presence of 2-order exceptional points, a topologically trivial band at the infinity can make the vibrational band topologically nontrivial. The symmetry, which is believed to be indispensable in topological models, is absent in this model. The fractional boundary states can be found in such classical system. Furthermore, the other aspect of the bulk boundary correspondence is revealed: an extra fractional exceptional point is topologically protected in bulk by the boundary states.