Exact Boundary Critical Exponents and Tunneling Effect in Integrable   Models for Quantum Wires
  Using the principles of the conformal quantum field theory and the finite size corrections of the energy of the ground and various excited states, we calculate the boundary critical exponents of single- and multicomponent Bethe ansatz soluble models. The boundary critical exponents are given in terms of the dressed charge matrix which has the same form as that of systems with periodic boundary conditions and is uniquely determined by the Bethe ansatz equations. A Luttinger liquid with open boundaries is the effective low-energy theory of these models. As applications of the theory, the Friedel oscillations due to the boundaries and the tunneling conductance through a barrier are also calculated. The tunneling conductance is determined by a nonuniversal boundary exponent which governs its power law dependence on temperature and frequency. 
Y. Wang, J. Voit, and F.-C. Pu