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Journal of Experimental and Theoretical Physics

Electric currents of excitations in the one-dimensional attractive Hubbard model

Sergey I. Matveenko

Published Jan 1, 1998• 1 citation
Publisher

Abstract

We have calculated electric currents of various types of excitations in the Hubbard model. Both spin and charge excitations carry the electric current. The electric charge is a continuous function of the band filling and the single-site repulsion potential.
DOI
10.1134/1.558475

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In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge ηηη-spin triplet excitations carry charge but no spin, and both spin-singlet and charge ηηη-spin-singlet excitations carry neither spin nor charge currents.
We have extended calculations of the zero-temperature excitation spectrum of the one-dimensional Hubbard model to the case where the number of electrons is less than the number of sites in the chain. The results are computed as a function of the ratio Ut\frac{U}{t}tU​, where UUU represents the on-site Coulomb repulsion and ttt is the transfer integral, assumed to be nonzero only for nearest neighbors. Exact calculations are made for the energy and momentum of excitations having single-particle character. Unlike the situation for the half-filled band, we find no gap in the excitation spectrum. We have also considered excitations of the spin-wave type. These are shown to vary linearly with momentum for small momentum. The group velocity for small momentum is found to be inversely proportional to the magnetic susceptibility.
The problem of spin-charge separation is addressed by considering current carrying states in a one-dimensional system of interacting electrons. Exact results for the Hubbard model and the bosonization method are exploited. We find that away from half filling both spin and charge excitations carry charge currents which are proportional to their momenta for most cases. Being in a qualitative agreement with the noninteracting ld Fermi gas picture, this result contradicts the spin-charge separation concept as it is usually derived e.g. from the bosonization approach or in a strong repulsion picture. For weak coupling the paradox is resolved by taking into account the Fermi velocity dispersion and by reexamining the structure of the current operator within the bosonization approach. For strong coupling we recover an effect of hale drag by a spinon as reflected in their momentum shifts.
We investigate the dynamical properties of the one-dimensional Hubbard model using the quantum Monte Carlo method and the numerical analytic continuation method based on the maximum entropy principle. Results for the spin, charge and current excitation spectrum are presented for various values of the coupling and the band filling for the system of 24 sites with the periodic boundary condition. We find that the total spectral density of the spin excitation exhibits a gapless structure irrespective of the coupling or the band filling. The charge excitation spectrum, on the other hand, clearly shows the gap formation at the half filled band and shifts its weight toward the higher energy region with increase of the coupling. This charge excitation gap, however, disappears with the hole doping. We also discuss the momentum dependence of the spectral functions.
Rigorous bounds on the susceptibilities of the single-band Hubbard model which hold in all dimensions are presented. In the attractive model the spin susceptibility is bounded above by (4\ensuremath{\Vert}U\ensuremath{\Vert}${)}^{\mathrm{\ensuremath{-}}1}$ where U(0) is the on-site interaction potential. In the half-filled repulsive model on a bipartite lattice the charge and the on-site pairing susceptibilities are bounded above by ${\mathit{U}}^{\mathrm{\ensuremath{-}}1}$. The present result implies that the susceptibilities never diverge in the above mentioned circumstances and also the absence of corresponding long-range order.