PLAQUETTE EXPANSION PROOF AND INTERPRETATION

The plaquette expansion, a general non-perturbative method for calcula ting the properties of lattice Hamiltonian systems, is established up to the first two orders for an arbitrary system. This method employs a n expansion of the Lanczos coefficients, the tridiagonal Hamiltonian m atrix elements or equivalently the continued fraction coefficients of the resolvent, in a descending series in the size of the system. The c oefficients of this series are formed from the low order cumulants or connected Hamiltonian moments. The lowest order approximation in the p laquette expansion corresponds to a gaussian model which is a conseque nce of the central limit theorem. The first nontrivial order yields a model with a spectrum on a bounded energy interval, becoming asymptoti cally uniform in the thermodynamic limit.