General nonperturbative estimate of the energy density of lattice Hamiltonians

Abstract

Employing a theorem on lower bounds on the zeros of orthogonal polynomials, the plaquette expansion to order 1/Np of the tridiagonal Lanczos matrix elements is solved for the ground-state energy density in the infinite lattice limit. The resulting nonperturbative expression for the estimate of the energy density in terms of the connected coefficients to order H4c is completely general. This expression is applied to various Hamiltonian systems the Heisenberg model in D dimensions and SU(2) and SU(3) lattice gauge theory in 3+1 dimensions. In all cases the analytic estimate to the energy density is not only a significant improvement on the trial state, but is typically accurate to a few percen..