Abstract
Treating the hole-magnon interaction within the self-consistent Born approximation, we demonstrate that the low-energy quasiparticles that occur in the t-J model due to quantum fluctuations of the spin system survive in the models including free hole propagation on the sublattices. The quasiparticle dispersion and weight are found to be strongly dependent on the next-neighbor hopping parameter. The flat band observed near the X point in the high-temperature superconductors is reproduced, but not for the realistic parameters that correspond to the hole-doped system.
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