Impurity in a Luttinger liquid: a numerical study of the finite size   energy spectrum and of the orthogonality catastrophe exponent
  The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density matrix renormalization group. By analyzing the finite size scaling behavior of the low energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. {\bf 68}, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the exponent of the orthogonality catastrophe, which gives a further support to the above theoretical prediction. 
Shaojin Qin (ICTP), Michele Fabrizio (SISSA), and Lu Yu (ICTP and   ITP-CAS)