Exact Boundary Critical Exponents and Tunneling Effect in Integrable Models for Quantum Wires

TL;DR

This paper calculates boundary critical exponents in integrable quantum wire models using conformal field theory and Bethe ansatz, revealing effects like Friedel oscillations and tunneling conductance behavior.

Contribution

It provides explicit formulas for boundary critical exponents in Bethe ansatz solvable models, linking them to the dressed charge matrix and low-energy Luttinger liquid theory.

Findings

Boundary critical exponents expressed via dressed charge matrix.

Friedel oscillations due to boundary effects.

Power-law tunneling conductance dependence on temperature and frequency.

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.