Lattice versus continuum theory of the periodic Heisenberg chain

We consider the detailed structure of low-energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the nonlinear corrections to the Gaussian model obtained from bosonization, we determine the exact coefficients of asymptotic expansions in inverse powers of the system length N for a large number of low-lying excited energy levels. This allows us to calculate eigenenergies of the lattice model up to order O(N-4), without having to solve the Bethe ansatz equations. At the same time, it is possible to express the exact eigenstates of the lattice model in terms of bosonic modes.