THE HALF-FILLED HUBBARD-MODEL IN THE PAIR APPROXIMATION OF THE CLUSTER VARIATION METHOD

The half-filled Hubbard model is studied in the pair approximation of the cluster variation method (CVM). The use of the SO(4) symmetry of t he model makes it possible to give a complete analytical characterizat ion of the ground state, by means of explicit expressions for the doub le occupancy and the nearest-neighbour correlation functions. The fini te-temperature analysis is reduced to the numerical solution of only t wo coupled transcendental equations. The behaviour of local magnetic m oment, specific heat and correlation functions is given for some typic al cases in one and two dimensions. We obtain good qualitative agreeme nt with exact and numerical results in one dimension. The results for finite temperatures show a rapid evolution, with increasing temperatur e, from a strongly antiferromagnetic behaviour to a disordered one; in the high-temperature region a maximum (which has been related to a 'g radual' metal-insulator transition) is found in the specific heat for very large values of the Coulomb repulsion.