Propriedades físicas de modelos integráveis

Abstract

In this thesis we tackled two di erent problems of quantum integrability. We derived nite sets of non-linear integral equations to describe physical properties of quantum chains invariant under the super-algebras su(2|1) and osp(1|2); and we also studied the in uence of boundary conditions on the bulk properties of the six-vertex model. The su(2|1) invariant model is a multi-chain generalization of the super-symmetric t-J model. Using the quantum transfer matrix method we obtained the phase diagram. For the osp(1|2) invariant model we could also rewrite the Hamiltonian in the language of itinerant fermions interacting through exchange, although the Hamiltonian itself is not hermitian, which corresponds to a non-unitary eld theory. We analytically computed the (e ective) central charge of this theory, corroborating numerical results of the literature. These results point towards the possibility of generalization of such non linear integral equations for models of di erent symmetries. Concerning the problem of the in uence of boundary conditions on the six-vertex model, we showed the existence of in nitely many boundaries whose intensive properties disagree with the standard periodic boundary condition SPBC = 32 ln(43). We also proved that by a suitable choice of boundary conditionsany entropy value in the interval [0, 12 ln(3324)] is accessible. We conjectured that the sameis true for the interval [ 1 2 ln(3324), SPBC]. The number of configurations of the six-vertex model with fixed boundary condition amounts to the enumeration problem of generalized alternating sign matrices.