The open XXZ and associated models at q root of unity
نویسنده
چکیده
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 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. 1 e-mail: [email protected]
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