Structural aspects of FRG in quantum tunneling computations

We probe both the unidimensional quartic harmonic oscillator and the double well potential through a numerical analysis of the Functional Renormalization Group flow equations truncated at first order in the derivative expansion. The two partial differential equations for the potential Vk(φ) and the wave function renormalization Zk(φ), as obtained in different schemes and with distinct regulators, are studied down to k=0, and the energy gap between lowest and first excited state is computed, in order to test the reliability of the approach in a strongly non-perturbative regime. Our findings point out at least three ranges of the quartic coupling λ, one with higher λ where the lowest order approximation is already accurate, the intermediate one where the inclusion of the first correction produces a good agreement with the exact results and, finally, the one with smallest λ where presumably the higher order correction of the flow is needed. Some details of the specifics of the infrared regulator are also discussed.