ANALYTIC SOLUTION FOR THE GROUND-STATE ENERGY OF THE EXTENSIVE MANY-BODY PROBLEM

A closed form expression for the ground-state energy density of the ge neral extensive many-body problem is given in terms of the Lanczos tri diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, alpha(n)(N) and beta(n)(N), asymptotic forms alpha(z) and beta(z) can be defined in terms of a parameter z drop n/N (n is the Lanczos itera tion and N is the size of the system). By application of theorems on t he zeros of orthogonal polynomials we find the ground-state energy den sity in the bulk limit to be given, in general, by epsilon(0) = inf[al pha(z) - 2 beta(z)].