Universal R operator with deformed conformal symmetry

We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The results for eigenvalues, eigenfunctions and integral kernel appear as deformations of the ones in the rational case. They provide a basis for the construction of integrable quantum systems generalizing the XXZ spin models to the case of arbitrary not necessarily finite-dimensional representations on the sites.Comment: 18 pages LaTex, revised, to be publ. in Nucl. Phy

A note on the boundary spin ss XXZ chain

The open spin $s$ XXZ model with non-diagonal boundaries is considered. Within the algebraic Bethe ansatz framework and in the spirit of earlier works we derive suitable reference states. The derivation of the reference state is the crucial point in this investigation, and it involves the solution of sets of difference equations. For the spin $s$ representation, expressed in terms of difference operators, the pseudo-vacuum is identified in terms of $q$-hypergeometric series. Having specified such states we then build the Bethe states and also identify the spectrum of the model for generic values of the anisotropy parameter $q$.Comment: 12 pages, Late

Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-S

The spin-1 Uimin-Lai-Sutherland (ULS) isotropic chain model is expressed in terms of fermions and the equivalence of the fermionic representation to the supersymmetric t-J model is established directly at the level of Hamiltonians.The spin-S ULS model is fermionized and the Hamiltonian of the corresponding generalisation of the t-J model is written down.Comment: 16 page

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