GENERALIZATION OF THE LUTTINGER THEOREM FOR FERMIONIC LADDER SYSTEMS

We apply a generalized version of the Lieb-Schultz-Mattis theorem to f ermionic ladder systems to show the existence of a low-lying excited s tate (except for some special fillings). This can be regarded as a non perturbative proof for the conservation under interaction of the sum o f the Fermi wave vectors of the individual channels, corresponding to a generalized version of the Luttinger theorem to fermionic ladder sys tems. We conclude by noticing that the Lieb-Schultz-Mattis theorem is not applicable in this form to show the existence of low-lying excitat ions in the limit that the number of legs goes to infinity, e.g., in t he limit of a 2D plane. [S0163-1829(98)04536-6].