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Progress of Theoretical Physics Supplement

Application of Conformal Field Theory to Electron Systems

N. Kawakami, Sung-Kil Yang

Published May 16, 2013• 0 citations
Publisher

Abstract

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

DOI
10.1143/ptp.106.157

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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.