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

TL;DR

This paper introduces an improved nonperturbative renormalization group method that maintains the full momentum dependence of correlation functions, enabling detailed analysis of quantum models and spectral functions with manageable computational effort.

Contribution

It develops a new approximation scheme that extends the local potential approximation by incorporating momentum-dependent derivative terms, facilitating the study of complex correlation functions.

Findings

Successfully applied to the 2D quantum O(N) model at zero temperature.

Enabled calculation of higher-order correlation functions like scalar susceptibility and conductivity.

Demonstrated the use of Padé approximants for analytic continuation to obtain spectral 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 $i\omega_n\to\omega+i0^+$ of imaginary frequency correlation functions $\chi(i\omega_n)$ computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.