We are studying low-dimensional quantum systems, from the view point of "instability and renormalization of the Tomonaga-Luttinger liquid (equivalent to c=1 conformal field theory)". Relating to this, it has been very difficult to analyze the Berezinskii-Kosterlitz-Thouless (BKT) transition with finite-size scaling method, since the divergence of the energy gap near the BKT transition is extremely slow, and there are logarithmic corrections. We have developed to overcome these difficulties, the "level spectroscopy".