The open XXZ andassociated models at q root of unity

Abstract

The generalized open XXZ model atq, a root of unity, is considered. We review how associated models, such as theq harmonic oscillator, and the lattice sine–Gordon and Liouville models are obtained.Explicit expressions for the local Hamiltonian of the spin XXZ spin chain coupled to dynamical degrees of freedom at one end of the chain are provided.Furthermore, the boundary non-local charges are given for the lattice sine–Gordon model and theq harmonic oscillator with open boundaries. We then identify the spectrumand the corresponding Bethe states of the XXZ model and theq harmonic oscillator in the cyclic representation with special non-diagonal boundaryconditions. Moreover, the spectrum and Bethe states of the lattice versions of thesine–Gordon and Liouville models with open diagonal boundaries are examined. The role ofthe conserved quantities (boundary non-local charges) in the derivation of the spectrum isalso discussed.