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The phase diagram of the Bose-Fermi Kondo model contains an SU(2)-invariantKondo-screened phase separated by a continuous quantum phase transition from aKondo-destroyed local moment phase. We analyze the effect of the Berry phaseterm of the spin path integral on the quantum critical properties of thisquantum impurity model. For a range of the power-law exponent characterizingthe spectral density of the dissipative bosonic bath, neglecting the influenceof the Berry phase term makes the fixed point Gaussian. For the same range ofthe spectral density exponent, incorporating the Berry phase term leads insteadto an interacting fixed point, for which a quantum to classical mapping breaksdown. Some general implications of our results are discussed.

Berry Phase and the Breakdown of the Quantum to Classical Mapping for the Quantum Critical Point of the Bose-Fermi Kondo model