Phase transitions on a ladder of braided non-Abelian anyons
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.
Keywords
Cite
@article{arxiv.1712.04179,
title = {Phase transitions on a ladder of braided non-Abelian anyons},
author = {Babatunde M. Ayeni and Robert N. C. Pfeifer and Gavin K. Brennen},
journal= {arXiv preprint arXiv:1712.04179},
year = {2018}
}
Comments
14 pages (double-column) and 8 figures. This paper is the completion of Chapter 6 of my PhD thesis (arXiv:1708.06476), though now with a number of changes