Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

Abstract

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot--Mend\'ez-Galain--Wschebor approximation scheme). As an application we consider the two-dimensional quantum O($N$) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the ``Higgs'' amplitude mode) and the conductivity. In particular, we show how, using Pad\'e approximants to perform the analytic continuation $i{\ensuremath{\omega}}_{n}\ensuremath{\rightarrow}\ensuremath{\omega}+i{0}^{+}$ of imaginary frequency correlation functions $\ensuremath{\chi}(i{\ensuremath{\omega}}_{n})$ computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.