Critical behaviour of integrable mixed spins chains

We construct a mixed spin 1/2 and S integrable model and investigate its finite size properties. For a certain conformal invariant mixed spin system the central charge can be decomposed in terms of the conformal anomaly of two single integrable models of spin 1/2 and spin (S − 1/2). We also compute the ground state energy and the sound velocity in the thermodynamic limit. Published in J.Phys.A:Math.Gen.26 (1993) L529 Integrable magnetic spin chains provide important examples of systems which can be derived from the so-called Yang-Baxter algebra [1]. A well known model is the isotropic spin 1/2 Heisenberg [2] chain and its generalization for arbitrary spin S [3, 4]. Another interesting example is the Heisenberg model in presence of an impurity of spin S [5, 6]. In such model one of the local vertex weight acts on a pair of asymmetric vector spaces which is defined by the local states on the horizontal and vertical lines of a two dimensional lattice. More recently, a general discussion concerning the construction of mixed vertex models has been presented by de Vega and Woynorovich [7]. For instance, they have studied several properties of the thermodynamic limit of an alternating anisotropic chain of spins 1/2 and 1. However, it is still to be investigated the finite size effects in these mixed spins models as well as their class of universality for conformally invariant systems. Following the approach of ref. [7] we construct an isotropic alternating spin 1/2 and S chain. We focus our attention in the analysis of the finite size behaviour of the ground state on a line of length L. A conformally invariant mixed system can be defined and its conformal anomaly is computed by analysing the finite size corrections for the ground state energy and by the thermodynamic Bethe ansatz. Several useful quantities as the ground state energy and the sound velocity are also computed. The construction of the transfer matrix of the mixed spins σ and S model is based on the local vertex R S,j(λ) which is a matrix in the auxiliary space Vσ and its matrix elements are operators of spin S acting on the Hilbert state space at site j. In the case of an auxiliary space of spin 1/2, R 1/2 S,j (λ) [8] is given by