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arXiv:0903.4574 · Journal of Physics B Atomic Molecular and Optical Physics

Scattering resonances and two-particle bound states of the extended Hubbard model

Manuel Valiente, David Petrosyan

Published Jun 1, 2009• 73 citations
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Abstract

We present a complete derivation of two-particle states of the one-dimensional extended Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and two families of energy-dependent interaction-bound states which are not present in the Hubbard model with the on-site interaction alone.

DOI
10.1088/0953-4075/42/12/121001

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We present a complete derivation of two-particle states of the one-dimensional extended Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and two families of energy-dependent interaction-bound states which are not present in the Hubbard model with the on-site interaction alone.
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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.
We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian Heff{H}_{\mathrm{eff}}Heff​ for hopping $t\ensuremath{\ll}V$ and arbitrary U<0.U<0.U<0. Retaining the most important terms, Heff{H}_{\mathrm{eff}}Heff​ can be mapped onto two XXZ\mathrm{XXZ}XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422n<0.422n<0.422 and $U<\ensuremath{-}4,$ singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{BiO}}_{3}.$