The open XXZ and associated models at q root of unity

Abstract

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 $\frac{1}{2}$ 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.

31 pages, LATEX, minor typos corrected

References in corpus (7)

• An integrable structure related with tridiagonal algebras
• A new (in)finite dimensional algebra for quantum integrable models
• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• One-boundary Temperley-Lieb algebras in the XXZ and loop models
• Equivalences between spin models induced by defects
• From affine Hecke algebras to boundary symmetries

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