Interacting anyons in topological quantum liquids: The golden chain

TL;DR

This paper explores a model of interacting Fibonacci anyons in a chain, revealing its critical behavior, conformal field theory description, and topological origin of gaplessness, advancing understanding of topological quantum liquids.

Contribution

It introduces a generalized anyonic spin chain model, maps it exactly to the tricritical Ising model, and demonstrates its criticality and topological gaplessness.

Findings

The anyonic chain is critical with central charge c=7/10.

The model maps onto the tricritical Ising conformal field theory.

The gapless nature of the chain has a topological origin.

Abstract

We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial (`identity') channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the two-dimensional tricritical Ising model is given using the restricted-solid-on-solid (RSOS) representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.