Spin-SS generalization of fractional exclusion statistics

We study fractional exclusion statistics for quantum systems with SU(2) symmetry (arbitrary spin $S$), by generalizing the thermodynamic equations with squeezed strings proposed by Ha and Haldane. The bare hole distributions as well as the statistical interaction defined by an infinite-dimensional matrix specify the universality class. It is shown that the system is described by the level-$2S$ WZW model and has a close relationship to non-abelian fractional quantum Hall states. As a low-energy effective theory, the sector of {\it massless} Z$_{2S}$ parafermions is extracted, whose statistical interaction is given by a finite-dimensional matrix.Comment: 11pages, REVTE

Alternating spin chains with singlet ground states

We investigate low-energy properties of the alternating spin chain model composed of spin $s_1$ and $s_2$ with a singlet ground state. After examining the spin-wave spectrum in detail, we map low-energy spin excitations to the O(3) non-linear sigma model in order to take into account quantum fluctuations. Analyzing the topological term in the resulting sigma model, we discuss how the massless or massive excitations are developed, especially according to the topological nature of the alternating spin system.Comment: 9 pages, revtex, to appear in PR

The open XXZ and associated models at q root of unity

The generalized open XXZ model at $q$ root of unity is considered. We review how associated models, such as the $q$ harmonic oscillator, and the lattice sine-Gordon and Liouville models are obtained. Explicit expressions of the local Hamiltonian of the spin ${1 \over 2}$ XXZ spin chain coupled to dynamical degrees of freedom at the one end of the chain are provided. Furthermore, the boundary non-local charges are given for the lattice sine Gordon model and the $q$ harmonic oscillator with open boundaries. We then identify the spectrum and the corresponding Bethe states, of the XXZ and the q harmonic oscillator in the cyclic representation with special non diagonal boundary conditions. Moreover, the spectrum and Bethe states of the lattice versions of the sine-Gordon and Liouville models with open diagonal boundaries is examined. The role of the conserved quantities (boundary non-local charges) in the derivation of the spectrum is also discussed.Comment: 31 pages, LATEX, minor typos correcte