Lattice Hamiltonian results for the spectrum of a (1 + 1)-dimensional asymptotically free field theory

Using lattice Hamiltonian methods, we investigate the spectrum of an asymptotically free field theory in 1 + 1 dimensions, the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ Thirring model. Lattice perturbation calculations are carried out to fourth order in the expansion parameter $\frac{1}{g^2}$. These calculations are extrapolated to the continuum (lattice spacing→0) using Padé approximants and are compared with the WKB results of Dashen, Hasslacher, and Neveu. Good agreement is found in many cases. The reliability of the Padé extrapolation method is studied by comparing several strong-coupling spectrum calculations with approximate mean-field calculations of the same quantities. The results are very encouraging.