A large-order analysis of one-dimensional lattice strong coupling expansions

A large order lattice strong coupling expansion for the ground state energy of the quantum mechanical hamiltonian 1/2p2 + gvertical strokexvertical strokesup(α), α > 0, is provided by a perturbative solution of the transfer matrix eigenvalue equation. This algorithmic derivation allows one to perform either an analytic or a very large order (N approx.= 50) numerical study of the expansion, which in particular is found to have a finite radius of convergence for α >= 2. These results, which can be useful for a better understanding of this model when treated as a quantum field theory, indicate that the continuum limit can be safely extracted but that the rate of convergence is generally very poor. (orig.)