Null states of the irreducible representations of the Virasoro algebra and hidden symmetries of the finite XXZ Heisenberg chain: A story about moving and frozen energy levels

Abstract

It is shown that the spectra of the spin- 1 2 anisotropic finite Heisenberg chain with boundary terms which depend on three parameters show, for special tuning of two of them unexpected symmetry properties, the U q [SU(2)] symmetry being a special case. We derive the tunings and the symmetry properties in the continuum limit and check them on the finite chains. A novel consequence of these symmetries is the observation that part of the energy levels of the chain with N − 1 sites coincide with some energy levels of the chain with N sites if the proper boundary terms are taken.