From spin to anyon notation: The XXZ Heisenberg model as a $D_{3}$ (or $su(2)_{4}$) anyon chain

TL;DR

This paper establishes a connection between the XXZ Heisenberg spin chain and a $D_{3}$ (or $su(2)_{4}$) anyon chain, highlighting how boundary conditions differentiate these models.

Contribution

It demonstrates how the XXZ Heisenberg model can be realized as a $D_{3}$ or $su(2)_{4}$ anyon chain, clarifying the role of boundary conditions.

Findings

The XXZ Heisenberg chain corresponds to a $D_{3}$/ $su(2)_{4}$ anyon model.

Boundary conditions are the primary difference between the models.

The relationship provides new insights into quantum spin and anyon chain correspondence.

Abstract

We discuss a relationship between certain one-dimensional quantum spin chains and anyon chains. In particular we show how the XXZ Heisenberg chain is realised as a $D_{3}$ (alternately $su(2)_{4}$) anyon model. We find the difference between the models lie primarily in choice of boundary condition.