Critical theories for the pseudogap Kondo problem

Abstract We discuss quantum phase transitions in the pseudogap Kondo problem, which describes a magnetic moment coupled to conduction electrons with a power-law density of states, ρ ( ω ) ∝ | ω | r . We show that different perturbative expansions, together with renormalization group techniques, provide effective low-energy field theories for the relevant critical fixed points. In particular, we review expansions near the lower- and upper-critical dimensions of the problem, being r = 0 and r = 1 , respectively.