Functional renormalization group for quantized anharmonic oscillator
Highlights: > RG analysis with field dependent wavefunction renormalization. > The Taylor expansion does not work for the wavefunction renormalization. > The gap energy is RG scheme-dependent. > The O (N) symmetric anharmonic oscillator exhibits only a single phase. > The evolution equation for the 2PI effective action for the oscillator is solved. - Abstract: Functional renormalization group methods formulated in the real-time formalism are applied to the O(N) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.