Method for calculating finite size corrections in Bethe ansatz systems: Heisenberg chain and six-vertex model

Abstract

A systematic procedure for computing large but finite size corrections in integrable theories is presented. It is based on an exact contour integral representation for the physical magnitudes. The saddle-point method applied to it provides the finite size corrections. We deal with the XXZ Heisenberg chain and the six-vertex model. The extension to any model solvable by the Bethe ansatz is straightforward provided the mass gap is not zero. The leading large size corrections for the two lowest lying states of the XXZ chain are derived in closed form. Leading finite size corrections to the excitations are obtained also.