Quantum Number Fractionalization in Antiferromagnets

In these lectures we shall derive and discuss a set of exact eigenstates of the Haldane—Shastry [1,2] model, a realization of the spin-1/2 Heisenberg chain in which the quantum-disordered spin liquid ground state and the neutral, spin-1/2 excitations of such systems are particularly easy to understand. This behavior is not unique to the model, and in particular occurs in the Bethe solution of the near-neighbour Heisenberg chain, where it was first discovered [3,4], but it is more accessible in this form. The model also makes the relationship of the spin chain to the fractional quantum Hall effect transparent [5]. The key results are shown in Fig. 3.1.