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Physical review. B, Condensed matter

Critical exponents of the SU(N) multicomponent Hubbard model and supersymmetrict-Jmodel in one dimension

Norio Kawakami

Published Feb 1, 1993• 32 citations
Publisher

Abstract

Using conformal field theory the exact critical exponents are obtained for the SU(N) generalization of the U\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard model and the supersymmetric t-J model in one dimension. For the Hubbard model the critical exponent of the momentum distribution function is given as \ensuremath{\theta}=(1-1/N${)}^{2}$/2 while for the supersymmetric t-J model \ensuremath{\theta} varies continuously in the range 0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}(1-1/N${)}^{2}$/2 depending on the electron concentration. The critical exponents of various correlation functions are shown to satisfy the universal scaling relations. The SU(N) t-J model in the range 0J/t\ensuremath{\le}2 belongs to the SU(N) Luttinger liquid for any finite N.

DOI
10.1103/physrevb.47.2928

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Using conformal field theory the exact critical exponents are obtained for the SU(N) generalization of the U\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard model and the supersymmetric t-J model in one dimension. For the Hubbard model the critical exponent of the momentum distribution function is given as \ensuremath{\theta}=(1-1/N)2{)}^{2})2/2 while for the supersymmetric t-J model \ensuremath{\theta} varies continuously in the range 0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}(1-1/N)2{)}^{2})2/2 depending on the electron concentration. The critical exponents of various correlation functions are shown to satisfy the universal scaling relations. The SU(N) t-J model in the range 0J/t\ensuremath{\le}2 belongs to the SU(N) Luttinger liquid for any finite N.
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The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.
The one-dimensional Hubbard model in a magnetic field is equivalent under renormalization-group transformation to a multicomponent Tomonaga-Luttinger model. The mapping between the Coulomb repulsion U of the Hubbard model and the couplings of the Tomonaga-Luttinger model is obtained for aribitrary magnetic field h and band filling n from a comparison of the correlation function exponents. These quantities are calculated for the Hubbard model from the finite-size corrections to the excitation energies, since the assumption of conformal invariance relates them to the critical exponents. On the other hand, the correlation functions of the multicomponent Tomonaga-Luttinger model are determined by solving the exact equation of motion derived by the use of generalized Ward identities.
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.