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arXiv:cond-mat/9602086 · Physical review. B, Condensed matter

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

Ying Wang, Johannes Voit, Fu‐Cho Pu

Published Sep 15, 1996• 45 citations
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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. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.8491

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The exact solution of the one-dimensional Hubbard model (for repulsive and attractive U)U)U) is used to calculate the tunneling rates of single electrons and Cooper pairs between two quantum wires. The critical exponents for the tunneling at small frequencies and low temperatures is obtained by means of the mesoscopic energy spectrum and conformal field theory. The situations of crossing wires, tunneling at a boundary, and resonant tunneling (through a bound state) are considered.
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We calculate the asymptotics of correlation functions for the one-dimensional model of fermions with correlated hopping recently proposed by the author. The method of calculation is based on predictions of conformal field theory, the Bethe ansatz solutions, and a finite-size analysis of the gapless excitations. The critical exponents are given in terms of dressed charge matrix. Components of this matrix are solutions of a set of integral equations obtained from the Bethe ansatz. The effective transport mass is calculated for an arbitrary band filling.
The critical properties of Tomonaga-Luttinger liquids including a mobile impurity are studied by means of the Bethe ansatz method, conformal field theory (CFT), and bosonization. We calculate conformal dimensions by performing the CFT analysis of the energy spectrum for an integrable impurity model, and show that this system is classified as c=1c=1c=1 shifted Gaussian CFT. The exact critical exponents of various correlation functions are obtained as functions of the impurity mass and its momentum. Passing to the continuum limit, we then construct an effective field theory in terms of bosonization, and directly calculate some correlation functions. A possible application to the Fermi-edge singularity in quantum wires is also discussed.