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The pseudogap Kondo problem, describing a magnetic impurity embedded in anelectronic environment with a power-law density of states, displays continuousquantum phase transitions between free and screened moment phases. In thispaper we employ renormalization group techniques to analytically calculateuniversal crossover functions, associated to these transitions, for variousobservables. Quantitative agreement with the results of NumericalRenormalization Group (NRG) simulations is obtained for temperature-dependentstatic and zero-temperature dynamic quantities, at and away from criticality.In the notoriously difficult realm of finite-temperature low-frequencydynamics, usually inaccessible to both NRG and perturbative methods, we showthat progress can be made by a suitable renormalization procedure in theframework of the Callan-Symanzik equations. Our general strategy can beextended to other zero-temperature phase transitions, both in quantum impuritymodels and bulk systems.Comment: 19 pages, 18 figures; (v3) version as publishe

Universal crossovers and critical dynamics of quantum phase transitions: A renormalization group study of the pseudogap Kondo problem