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Exact results with the Kotliar-Ruckenstein slave-boson representation

Radial slave boson representations have the particular advantage that the expectation values of their respective fields are finite even without the formal introduction of spurious Bose condensates for each of the bosonic fields. The expectation values of the radial (real) fields are in fact to be interpreted as the density of empty or singly occupied sites. Whereas the radial representation of the Barnes slave bosons has been investigated before, a setup for the functional integral of radial bosonic fields in the more physical Kotliar-Ruckenstein representation has not been accomplished to date. We implement a path integral procedure with suitable renormalization factors for a strongly correlated two-site model which allows to control the formal steps in the intricate evaluation, as the results for the partition function and the expectation values are known from exact diagonalization for such a minimal single impurity Anderson model. The partition function is shown to be a trace over a product of matrices local in time and therefore can be calculated analytically. Eventually, we establish the scheme for the evaluation of correlation functions and thermodynamic properties.