The dispersion relation of a doped hole in the half-filled 2D Hubbard model is shown to follow a |k|4 law around the (0, ± π) and (±π, 0) points in the Brillouin zone. Upon addition of pair-hopping processes this dispersion relation is unstable towards a |k|2 law. The above follows from T = 0 Quantum Monte-Carlo calculations of the single particle spectral function A(k., ω) on 16 × 16 lattices. We discuss finite dopings and argue that the added term restores coherence to charge dynamics and drives the system towards a dx2-y2 superconductor.
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