  We discuss how to construct models of interacting anyons by generalizing
quantum spin Hamiltonians to anyonic degrees of freedom. The simplest
interactions energetically favor pairs of anyons to fuse into the trivial
("identity") channel, similar to the quantum Heisenberg model favoring pairs of
spins to form spin singlets. We present an introduction to the theory of anyons
and discuss in detail how basis sets and matrix representations of the
interaction terms can be obtained, using non-Abelian Fibonacci anyons as
example. Besides discussing the "golden chain", a one-dimensional system of
anyons with nearest neighbor interactions, we also present the derivation of
more complicated interaction terms, such as three-anyon interactions in the
spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg
ladders. We also discuss generalizations to anyons with general non-Abelian
su(2)_k statistics. The k to infinity limit of the latter yields ordinary SU(2)
spin chains.
