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

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