Evolution of the magnetization after a local quench in the critical   transverse-field Ising chain
  We study the time evolution of the local magnetization in the critical Ising chain in a transverse field after a sudden change of the parameters at a defect. The relaxation of the defect magnetization is algebraic and the corresponding exponent, which is a continuous function of the defect parameters, is calculated exactly. In finite chains the relaxation is oscillating in time and its form is conjectured on the basis of precise numerical calculations. 
F. Igl\'oi, G. Ro\'osz and L. Turban
cond-mat.stat-mech quant-ph