Quantum spin-3/2 models on the Cayley tree - optimum ground state approach

We present a class of optimum ground states for quantum spin-3/2 models on the Cayley tree with coordination number 3. The interaction is restricted t o nearest neighbours and contains 5 continuous parameters. For all values o f these parameters the Hamiltonian has parity invariance, spin-flip invaria nce, and rotational symmetry in the xy-plane of spin space. The global grou nd states are constructed in terms of a 1-parametric vertex state model, wh ich is a direct generalization of the well-known matrix product ground stat e approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudi nal and transversal two-point correlation functions.