Functional renormalization group for quantized anharmonic oscillator

TL;DR

This paper applies real-time functional renormalization group methods to analyze the quantum anharmonic oscillator, revealing a single symmetric phase and scheme-dependent infrared behavior of couplings.

Contribution

It introduces a real-time FRG approach to the quantum anharmonic oscillator and investigates scheme dependence and phase structure at next-to-leading order.

Findings

Existence of only a single, symmetric phase.

Field-dependent wavefunction renormalization is noticeable.

Infrared limits of couplings depend on the renormalization scheme.

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 field-independent term of the wavefunction renormalization turned out to be negligible, but its field-dependent piece is noticeable. It is shown that the infrared limits of the running couplings depend on the renormalization group scheme used, when the perturbation expansion in the bare quartic coupling is truncated keeping the terms up to the second order.