The authors present a method of calculating finite-size corrections for the isotropic (XXX) Heisenberg chain in the antiferromagnetic case. The leading corrections to the energy and the root density of the ground state are compared with the numerical data up to N=256 sites in the chain.
Leading and next-to-leading-order finite-size corrections to the ground and first excited states are calculated for the spin-1/2 anisotropic Heisenberg model in the critical region. The analytic results are compared to numerical data obtained for chains up to a length of N=1024. It is found that, near the isotropic point, the asymptotic region where the results obtained for N to infinity are applicable sets in at very large N values, and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms, even at large (N>100) chain lengths.