The XXZ chain

Abstract

The XXZ spin chain is an integrable generalization of the Heisenberg chain that accounts for a uni-axial anisotropy in the spin interaction. Its Bethe Ansatz solution is a “straightforward” generalization of the one employed in the previous chapter, but the classification of complex roots is more involved and the nature of the low energy excitations changes with the anisotropy. After previewing the phase diagram of the chain in Sect. 4.1, we recap the coordinate Bethe Ansatz solution in Sect. 4.2. We then analyze the different phases in Sects. 4.3, 4.4, and 4.5, by focusing on the physical properties and skipping some technical derivations.