Quasiparticles in quantum spin chains with strong axial exchange anisotropy
The quasiparticle composition of the eigenstates of quantum spin chains with nearest-neighbor exchange coupling subject to strong axial anisotropy is the focus of this dissertation. Complementary sets of quasiparticles are generated from opposite ends of the spectrum for the systematic generation of all eigenstates. The exclusion statistics of all quasiparticles thus introduced are determined exactly and used, in selected cases, for the exact thermodynamic analysis of the underlying spin chain model. This project starts from the Ising model with spin s = 1/2 and then branches out to the spin s = 1/2 XXZ model in the axial regime and to the spin s = 1 Ising model. In the s = 1/2 Ising case, the two complementary sets of quasiparticles are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s = 1 Ising case, they are soliton pairs and nested strings, respectively. The string quasiparticles of the s = 1/2 Ising chains are identified as limiting cases of Bethe ansatz solutions of the axial XXZ model. The thermodynamics of the Ising chain for s 1/2 is shown to be equivalent to that of a system of two species of solitons and for s = 1 to that of a system of six species of soliton pairs. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to M lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M → ∞, to the thermodynamics of the s = 1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s = 1/2 XXZ chain. The exclusion statistics is semionic for both spinons and solitons but the spinon vacuum is unique whereas the soliton vacuum is twofold with broken symmetry.