  The one-dimensional Holstein model of spinless fermions interacting with
dispersionless phonons is studied using a new variant of the density matrix
renormalisation group. By examining various low-energy excitations of finite
chains, the metal-insulator phase boundary is determined precisely and agrees
with the predictions of strong coupling theory in the anti-adiabatic regime and
is consistent with renormalisation group arguments in the adiabatic regime. The
Luttinger liquid parameters, determined by finite-size scaling, are consistent
with a Kosterlitz-Thouless transition.
