Fermi and non-Fermi Liquid Behavior in Quantum Impurity Systems: Conserving Auxiliary Particle Theory

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We review a recently developed method, based on an exact auxiliary boson representation, to describe both Fermi liquid and non-Fermi liquid behavior in quantum impurity systems. Coherent spin and charge fluctuation processes are taken into account in a self-consistent way and are shown to include all leading and subleading infrared singularities at any given order of the self-consistent loop expansion of the free energy. As a consequence, for the SU(N)× SU(M) Anderson impurity models the correct temperature dependence of the susceptibility is recovered over the entire temperature range, including Fermi liquid or non-Fermi liquid behavior below the Kondo temperature Tₖ. As a standard diagram technique the presented method has the potential to be generalized to correlated electron systems on a lattice.