Russian doll spectrum in a non-Abelian string-net ladder

TL;DR

This paper investigates the phase diagram of a non-Abelian string-net ladder with string tension, revealing a unique Russian doll spectrum with size-independent energy levels and exact gap calculations at self-dual points, contrasting with Fibonacci or Ising models.

Contribution

It introduces the first analysis of a non-Abelian string-net ladder with a detailed spectrum, highlighting the Russian doll structure and exact solutions at self-dual points.

Findings

Discovery of a Russian doll spectrum with size-independent energy levels.

Exact gap calculation at self-dual points using Temperley-Lieb mapping.

Contrasts with Fibonacci and Ising theories in spectral properties.

Abstract

We study a string-net ladder in the presence of a string tension. Focusing on the simplest non-Abelian anyon theory with a quantum dimension larger than two, we determine the phase diagram and find a Russian doll spectrum featuring size-independent energy levels as well as highly degenerate zero-energy eigenstates. At the self-dual points, we compute the gap exactly by using a mapping onto the Temperley-Lieb chain. These results are in stark constrast with the ones obtained for Fibonacci or Ising theories.