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arXiv:cond-mat/9307019 · International Journal of Modern Physics B

SPECTRUM OF LOW-LYING EXCITATIONS IN A SUPERSYMMETRIC EXTENDED HUBBARD MODEL

Fabian H. L. Eßler, V. E. Korepin

Published Oct 20, 1994• 32 citations
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Abstract

We continue the study of the u(2|2)-supersymmetric extension of the Hubbard model in one dimension. We determine the excitation spectrum at zero temperature even in the sectors where the ground states are u(2|2)-descendants of Bethe states. The excitations include spinons, holons, electrons, localons (local electron pairs, moving coherently through the lattice) and their bound states. The spectra are found to be very different for repulsive and attractive on-site interaction. We also study the thermodynamics of the model.

DOI
10.1142/s0217979294001366

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The thermodynamic Bethe-ansatz equations for the one-dimensional Hubbard model are derived for an attractive on-site interaction of the electrons, extending in this way Takahashi's result for the repulsive Hubbard chain. The results are discussed in several special limits, e.g., interaction much larger than the hopping, U\ensuremath{\rightarrow}0 case, and the high- and low-temperature limits. The dominating states at low temperatures consist of spin-paired electrons (resembling Cooper pairs) and bound states of such pairs. The excitation spectrum and its properties are discussed in the context of superconductivity and resonant valence bonds.
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The one dimensional t-J Hamiltonian is diagonalized exactly for the supersymmetric case 2t=\ifmmode\pm\else\textpm\fi{}J using the Bethe ansatz. In this limit it is identical with models previously considered by Lai, Sutherland, and Schlottmann. In the present paper we discuss the ground-state properties and excitation spectrum in zero magnetic field. The ground state is a liquid of singlet bonds with varying spatial separation. Its most remarkable feature is the presence of bonds connecting particles at arbitrarily large distances. The ground-state energy is an analytic function of the band filling. There is no difference in the chemical potential for adding one or two particles and no evidence for the binding of holes. The low-lying part of the spectrum consists of two types of gapless excitations (charge and spin) with effective Fermi surfaces at 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.
A Hubbard-like model with SU(4) symmetry for electrons with twofold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two electrons. The features of ground state and excited states for repulsive coupling are shown. For finite NNN number of electrons, the configurations of quantum numbers are given explicitly and the spectra of excitations are obtained by solving Bethe-ansatz equation numerically. For infinite N,N,N, the ground state and various kinds of low-lying excitations are obtained on the basis of thermodynamics limit.