Gap-formation mechanism of the Kondo-necklace model

We investigate a gap-formation mechanism of the one-dimensional Kondo-necklace model at zero temperature. An analytic treatment using the bosonization method shows that the model undergoes the Kosterlitz-Thouless transition at the critical coupling $J_c=0\mathrm{}$, which is described by the quantum sine-Gordon model. This result is contrary to the previous investigations on the ground-state phase transition, where some finite critical coupling values have been predicted. To clarify the validity of our analytic calculation result, we estimate the singlet-triplet gap by employing White's density matrix renormalization group method; the numerical calculation is carried out for the systems up to 200 sites with open boundary condition. As a result, we find that the excitation gap observed in the large $J$ region becomes smaller quickly with the decrease of $J$. However, the data show the existence of a small gap for $J>~0.25$, which seems to support $J_c=0\mathrm{}$.