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arXiv:hep-th/0306173 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Comment on “Properties of the massive Thirring model fromXYZspin chain”

Takehisa Fujita, Takuya Kobayashi, Hidenori Takahashi

Published Sep 3, 2003• 2 citations
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Abstract

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.
DOI
10.1103/physrevd.68.068701

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A procedure is presented to obtain finite temperature excitations of the XYZ spin chain. Numerical results agree with the analytic expressions derived by Johnson, Kinsky and McCoy at T=0. The numerical results also agree with those of the Heisenberg-Ising ring by Johnson at T ≠ 0. Sample dispersion curves are illustrated for the “scaling region”, which is expected to have and equivalence to the massive Thirring model. Temperature dependences are calculated for some types of elementary excitations.
The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe ansatz for the eigenstates. The physical states are described by many-body wave functions representing the vacuum as a filled Fermi-Dirac sea and particle states as excitations built upon it. The spectrum of states is determined by imposing periodic boundary conditions on the wave functions. The energies are calculated by reducing the periodic boundary conditions to linear integral equations. For fermion-antifermion bound states the Dashen-Hasslacher-Neven spectrum is obtained. It is shown that the solution to the massive Thirring model can be understood as the critical limit of Baxter's solution of the eight-vertex model.