Phase transitions on a ladder of braided non-Abelian anyons

TL;DR

This paper investigates the impact of non-Abelian anyonic statistics on quantum phases using a Hubbard model on a ladder, revealing complex phase diagrams and the distinct roles of fusion and braid statistics.

Contribution

It introduces a novel anyonic Hubbard model on a ladder incorporating braiding and Heisenberg interactions, analyzing Fibonacci and Ising anyons.

Findings

Rich phase diagrams for Fibonacci and Ising anyons

Distinct roles of fusion and braid statistics in phase formation

Identification of new quantum phases influenced by anyonic statistics

Abstract

Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between anyons has been well studied. However, unlike our understanding of the role of bosonic and fermionic statistics in the formation of different quantum phases of matter, little is known concerning the effect of non-Abelian anyonic statistics. We explore this physics using an anyonic Hubbard model on a two-legged ladder which includes braiding and nearest neighbour Heisenberg interactions among anyons. We study two of the most prominent non-Abelian anyon models: the Fibonacci and Ising type. We discover rich phase diagrams for both anyon models, and show the different roles of their fusion and braid statistics.