Exact boundary critical exponents and tunneling effects in integrable models for quantum wires

Abstract

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. © 1996 The American Physical Society.