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 general extensive many-body problem is given in terms of the Lanczos tridiagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, an(N) and bn(N), asymptotic forms a(z) and b(z) can be defined in terms of a parameter z[n/N (n is the Lanczos iteration and N is the size of the system!. By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given, in general, by E05inf@a(z)22b(z)# . @S0163-1829~96!07044-0#