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Progress of Theoretical Physics Supplement

Application of Conformal Field Theory to Electron Systems

Norio Kawakami, Sung-Kil Yang

Published Jan 1, 1991• 2 citations
Publisher

Abstract

Recent progress in conformal field theory enables us to precisely treat the critical phenomena in (1 +I)-dimension. We review how conformal field theory applies to correlated electron systems in one dimension and explain the way of exact calculation of the correlation exponents. We demonstrate that conformal field theory provides the microscopic foundation of the Luttinger liquid which describes the universal behavior of lD correlated electron systems.

DOI
10.1143/ptps.106.157

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Recent progress in conformal field theory enables us to precisely treat the critical phenomena in (1 +I)-dimension. We review how conformal field theory applies to correlated electron systems in one dimension and explain the way of exact calculation of the correlation exponents. We demonstrate that conformal field theory provides the microscopic foundation of the Luttinger liquid which describes the universal behavior of lD correlated electron systems.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.
In 1950, Tomonaga published a pioneering paper on collective motion of interacting fermions in one spatial dimension, which now establishes the basic concept of one-dimensional quantum critical phenomena, the so-called Tomonaga-Luttinger liquid. We briefly discuss fundamental properties of the Tomonaga-Luttinger liquid in comparison with the Fermi liquid. We then explain how (1+1) dimensional conformal field theory can be used to describe universal properties of the Luttinger liquid. Some examples of recent experimental observations are also addressed.
We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Ferimi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the one-dimensional Fermi-liquid theory. Exact correspondence between the Landau parameters and Haldane parameters is established. The exponents of the dynamical correlation functions and the impurity problem are also discussed based on the finite size corrections of elementary excitations with the predictions of the conformal field theory, which provides a bridge between the one-dimensional Fermi-liquid and the Luttinger liquid.