BETHE ANSATZ RESULTS FOR HUBBARD CHAINS WITH TOROIDAL BOUNDARY-CONDITIONS

We solve exactly the problem of a one-dimensional repulsive-U Hubbard chain with toroidal boundary conditions (HTB) using the Bethe ansatz approach. We calculate analytically the finite-size corrections to the ground-state energy in the half-filled case and use this expression to derive charge and spin stiffnesses with no assumptions. We then use a "particle-hole" transformation to calculate the finite-size corrections for the half-filled attractive-U case, and again derive the resulting expressions for the charge and spin stiffnesses. Lastly, we discuss how the repulsive-U corrections relate to those of a Heisenberg model with toroidal boundary conditions.