Combining complex and radial slave boson fields within the Kotliar-Ruckenstein representation of correlated impurities

TL;DR

This paper develops a method combining complex and radial slave boson fields within the Kotliar-Ruckenstein framework to improve the treatment of correlated impurities, verified by exact solutions of the Hubbard model in the atomic limit.

Contribution

It introduces a procedure for functional integration of constrained fermionic, complex, and radial bosonic fields in the Kotliar-Ruckenstein representation.

Findings

Exact evaluation of the partition function in the atomic limit confirms the method's correctness.

Elimination of spurious Bose condensations improves the saddle-point approximation.

The approach enhances the theoretical description of correlated impurity systems.

Abstract

The gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle-point approximation is performed. Within the Kotliar-Ruckenstein representation, three of the four bosonic fields can be radial while the last one has to remain complex. In this work, we present the procedure to carry out the functional integration involving constrained fermionic fields, complex bosonic fields, and radial bosonic fields. The correctness of the representation is verified by exactly evaluating the partition function and the Green's function of the Hubbard model in the atomic limit.