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Physical review. B, Condensed matter

Critical exponents for a one-dimensional model of fermions with correlated hopping

Igor N. Karnaukhov

Published Mar 15, 1995• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.51.7858

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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.
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Using results on the scaling of energies with the size of the system and the principles of conformal quantum field theory, we calculate the asymptotics of correlation functions for the one-dimensional Hubbard model in the repulsive regime in the presence of an external magnetic field. The critical exponents are given in terms of a dressed charge matrix that is defined in terms of a set of integral equations obtained from the Bethe-Ansatz solution for the Hubbard model. An interpretation of this matrix in terms of thermodynamical coefficients is given, and several limiting cases are considered.
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.
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One parametric one-dimensional spinless fermion models is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interactions. The ground state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.
One parametric one-dimensional spinless fermion model is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many-particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interaction. The ground-state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.