Two Particle Scattering and Orthogonality Catastrophy in the Hubbard Model
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The wavefunction of two fermions subject to a repulsive Hubbard interaction in the presence of a Fermi sea is evaluated in detail. As first shown by Anderson, in some cases the wavefunction may be affected by scattering even if both particles are situated on the Fermi surface. A direct signal for an orthogonality catastrophy produced by interactions of an extra particle with the rest of the system is however found only in one dimension. Nevertheless, the structure of the interacting two-particle wavefunction suggests the possibitiy of new non-perturbative phenomena in the 2D Hubbard model.
KeywordsFermi Surface Hubbard Model Fermi Point Double Occupancy Local Scatterer
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