Possibility of quasiparticle behaviour in the strongly correlated Hubbard model

Abstract

The author calculates an exact expression for the Green function of a single hole in a Neel background, for finite Ising interaction Jz identical to 4t2/U where t is the hopping (overlap) integral in the Hubbard model and U the usual on-site interaction. In 1D for fixed boundary conditions, loops are absent and thus the expression is exact and independent of the retraceable path approximation, while in 2D the expression is exact to within the exclusion of loops. The spectral function A( omega ) shows delta-function peaks at well defined energy spacings, with damping only at frequencies omega >5/2Jz different from earlier results. These peaks are necessary for the existence of quasiparticles. The author presents an argument that, for sufficiently large U, the discrete spectrum in A( omega ) merges to a continuous 'band' as the weight varies as Jz of the poles vanishes in the U= infinity limit and hence that use of the latter does not necessarily imply incoherent behaviour in the system.