Universal properties of anyon braiding on one-dimensional wire networks

TL;DR

This paper explores how anyons on one-dimensional wire networks exhibit diverse braiding behaviors influenced by network topology, revealing new possibilities for non-abelian statistics and their dependence on network connectedness.

Contribution

It uncovers the topological dependence of anyon braiding on wire network connectedness, showing how network structure affects particle statistics and linking 1D systems to 2D braiding properties.

Findings

Braiding properties vary with network connectedness.

Particles can change statistics when moving between modules.

Highly connected networks replicate 2D braiding behaviors.

Abstract

We demonstrate that anyons on wire networks have fundamentally different braiding properties than anyons in 2D. Our analysis reveals an unexpectedly wide variety of possible non-abelian braiding behaviours on networks. The character of braiding depends on the topological invariant called the connectedness of the network. As one of our most striking consequences, particles on modular networks can change their statistical properties when moving between different modules. However, sufficiently highly connected networks already reproduce braiding properties of 2D systems. Our analysis is fully topological and independent on the physical model of anyons.