Comment on " the Massive Thirring Model from Xyz Spin Chain " by Kolanovic Et Al

It is shown that the continuum limit of the spin 1/2 Heisenberg XYZ model is far from sufficient for the site number of 16. Therefore, the energy spectrum of the XYZ model obtained by Kolanovic et al. has nothing to do with the massive Thirring model, but it shows only the spectrum of the finite size effects. The spin 1/2 Heisenberg model is a rich theory, which contains a variety of field theories in the continuum limit. In particular, the Heisenberg XYZ model is proved to be equivalent to the massive Thirring model in the continuum limit. Recently, Kolanovic, Pallua and Prester [1] solved the Heisenberg XYZ model numerically to study the bound state problem in the massive Thirring model. In [email protected] [email protected] [email protected] 1 their paper, they claim that the binding energies of the bosonic states in the massive Thirring model are consistent with those of the semiclassical calculations by Dashen et al.[2], contrary to the predictions by Fujita et al. [3-5]. In this comment, we show that the calculation of Kolanovic et al.[1] is far from reliable due to the rough resolution of their calculations. That is, the energy resolution in their calculation is not smaller than the mass parameter they used, and therefore there is no chance to obtain the binding energy of the system which should be in the continuum limit. The spectrum they obtain is nothing but some factor times the resolution 2π/L. Now, the spin 1/2 Heisenberg XYZ model can be described by the following hamiltonian, H = N