BKT transition and level spectroscopy
  Berezinskii-Kosterlitz-Thouless (BKT) transition is one of the instability mechanisms for the Tomonaga-Luttinger liquid.   But in the BKT transition, there are logarithmic-correction problems, which make it very difficult to treat BKT transitions numerically.   We propose a method, ``level spectroscopy'', to overcome such difficulties, based on the renormalization group analysis and the symmetry consideration. 
Kiyohide Nomura and Atsuhiro Kitazawa