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Journal of Physics A Mathematical and General

Elementary excitations in the Hubbard model with boundaries

Hitoshi Asakawa, Masuo Suzuki

Published Jun 7, 1997• 9 citations
Publisher

Abstract

Elementary excitations in the one-dimensional Hubbard model with boundaries are discussed at the half-filling and without external magnetic fields. The energy of the present model is evaluated in the low-lying excited state, where there exist quasiparticles corresponding to elementary excitations in the charge and the spin sectors. The boundary scattering matrix of the quasiparticles is evaluated.

DOI
10.1088/0305-4470/30/11/008

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Elementary excitations in the one-dimensional Hubbard model with boundaries are discussed at the half-filling and without external magnetic fields. The energy of the present model is evaluated in the low-lying excited state, where there exist quasiparticles corresponding to elementary excitations in the charge and the spin sectors. The boundary scattering matrix of the quasiparticles is evaluated.
We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states of four elementary excitations, which form the fundamental representation of SU(2)\ifmmode\times\else\texttimes\fi{}SU(2). We evaluate the exact S matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.
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 present single-particle and thermodynamic properties of the half-filled single-band Hubbard model in 2D calculated in the self-consistent fluctuation exchange approximation. The low-energy excitations at moderate temperatures and small UUU are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in $\mathrm{Re}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})$ and a local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})|$ at $\ensuremath{\varepsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. We explain these results using a simple spin-fluctuation model.