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arXiv:cond-mat/9512056

Superconducting correlation in the one-dimensional $t$-$J$ model with anisotropic spin interaction and broken parity

Shiraishi, J., Yoshifumi Morita, Mahito Kohmoto

Published Dec 8, 1995• 0 citations
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Abstract

A variant of the one-dimensional $t$-$J$ model with anisotropic spin interaction and broken parity is studied by the nested algebraic Bethe-ansatz method. The gapless charge excitations and the gapful spin excitations are obtained. It is shown that the singlet-superconducting correlation dominates in the low-density region by applying the finite-size scaling analysis in the conformal field theory.

DOI
10.48550/arxiv.cond-mat/9512056

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Superconducting correlation in the one-dimensional ttt-JJJ model with anisotropic spin interaction and broken parity
A variant of the one-dimensional ttt-JJJ model with anisotropic spin interaction and broken parity is studied by the nested algebraic Bethe-ansatz method. The gapless charge excitations and the gapful spin excitations are obtained. It is shown that the singlet-superconducting correlation dominates in the low-density region by applying the finite-size scaling analysis in the conformal field theory.
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.
We investigate the excitation spectrum of a model of N colour fermions with correlated hopping which can be solved by a nested Bethe ansatz. The gapless excitations of particle-hole type are calculated as well as the spin-wave like excitations which have a gap. Using general predictions of conformal field theory the long distance behaviour of some ground state correlation functions are derived from a finite-size analysis of the gapless excitations. From the algebraic decay we show that for increasing particle density the correlation of so-called N-multiplets of particles dominates over the density-density correlation. This indicates the presence of bound complexes of these N-multiplets. This picture is also supported by the calculation of the effective mass of charge carriers.
An exact solvable model of the coupled supersymmetric t - J chains interacting via the spin exchange interaction is proposed and solved by the means of the nested Bethe ansatz. It is shown, that in addition to the direct spin-exchange interaction an effective interaction between fermions of different chains called as "an effective attractive hard-core interaction" is realized in the model. The critical exponents describing asymptotic behavior of the correlation functions are calculated using the Bethe ansatz equations and the finite-state scaling analysis in conformal field theory. It is shown that the two-component Tomonaga-Luttinger liquid with the dominating correlations of fermion pairs is realized in the low-density region. This non-traditional behavior of the correlation functions is realized due to the effective attractive hard-core interaction between particles.
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.