The spin-1/2 XXZ Heisenberg chain, the quantum algebra Uq[sl(2)], and duality transformations for minimal models

The finite-size spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with central charge c<1 including the unitary and the non-unitary minimal series. Taking into account the half--integer angular momentum sector-which correspond to chains with an odd number of sites-in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chains corresponds to a new type of frustration lines in the projected minimal models. The corresponding new boundary conditions in the hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operator involved. Related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite XXZ chain. The observed degeneracies in energy and in momentum spectra are shown to the consequence of interviewing relations Uq[sl(2)] quantum algebra transformations. (author)