Quantitative expression of the spin gap via bosonization for a dimerized   spin-1/2 chain
  Using results on the mass gap in the sine-Gordon model combined with the exact amplitudes in the bosonized representation of the Heisenberg spin-1/2 chain and one-loop renormalization group, we derive a quantitative expression for the gap in a dimerized spin-1/2 chain. This expression is shown to be in good agreement with recent numerical estimates when a marginally irrelevant perturbation is taken into account. 
Edmond Orignac