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Gutzwiller Variational Method for Intersite Coulomb Interactions: The Spinless Fermion Model in One Dimension

We study the Gutzwiller method for the spinless fermion model in one dimension, which is one of the simplest models that incorporates the intersite Coulomb interaction. The Gutzwiller solution of this model has been studied in the literature but with differing results. We obtain the Gutzwiller solution of the problem by a careful enumeration of the many-particle configurations and explain the origin of the discrepancy in the literature to be due to the neglect of the correlation between the neighbouring bond occupancies. The correct implementation of the Gutzwiller approach yields results different from the slave-boson mean-field theory, unlike for the Hubbard model with on-site interaction, where both methods are known to be equivalent. The slave-boson and the Gutzwiller results are compared to the exact solution, available for the half-filled case, and to the numerical exact diagonalization results for the case of general filling.