Truncated conformal space at c=1, nonlinear integral equation and quantization rules for multi-soliton states

We develop truncated conformal space (TCS) technique for perturbations of c=1 conformal field theories. We use it to give the first numerical evidence of the validity of the non-linear integral equation (NLIE) derived from light-cone lattice regularization at intermediate scales. A controversy on the quantization of Bethe states is solved by this numerical comparison and by using the locality principle at the ultraviolet fixed point. It turns out that the correct quantization for pure hole states is the one with half-integer quantum numbers originally proposed by Fioravanti et al. [Phys. Lett. B 390 (1997) 243]. Once the correct rule is imposed, the agreement between TCS and NLIE for pure hole states turns out to be impressive.