Non-Abelian statistics as a Berry phase in exactly solvable models

TL;DR

This paper introduces a method to directly observe non-Abelian statistics in exactly solvable quantum models using Berry phases, confirming the existence of non-Abelian anyons in Kitaev's honeycomb model and proposing experimental detection techniques.

Contribution

The paper presents a novel approach to study non-Abelian statistics via Berry phases in exactly solvable models, with explicit demonstrations and experimental proposals.

Findings

Confirmed non-Abelian Ising anyons in Kitaev's model

Demonstrated Berry phase as a signature of non-Abelian statistics

Provided predictions for experimental detection in realistic systems

Abstract

We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasiparticles, the resulting Berry phase provides a direct demonstration of their non-Abelian statistics. We apply this technique to Kitaev's honeycomb lattice model and explicitly demonstrate the existence of non-Abelian Ising anyons confirming the previous conjectures. Finally, we present the manipulations needed to transport and detect the statistics of these quasiparticles in the laboratory. Various physically realistic system sizes are considered and exact predictions for such experiments are provided.