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--Mendéz-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 Padé approximants to perform the analytic continuation $i{\omega }_n\to \omega +i{0}^{+}$ 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.

19 pages, 10 figures. Final version

References in corpus (14)

• Exact evolution equation for the effective potential
• The critical exponents of the superfluid transition in He4
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Non-perturbative finite-temperature Yang-Mills theory
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Critical capacitance and charge-vortex duality near the superfluid to insulator transition
• Dynamical response near quantum critical points
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Spectral Functions from the Functional Renormalization Group
• Superuniversal transport near a $(2+1)$-dimensional quantum critical point
• Effective average action based approach to correlation functions at finite momenta
• Spectral functions from the functional renormalization group at finite temperature and density
• Duality-mediated critical amplitude ratios for the $(2+1)$-dimensional $S=1$ $XY$ model

Cited by in corpus (9)

• The nonperturbative functional renormalization group and its applications
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Scheme dependence of asymptotically free solutions
• Critical $O(2)$ field theory near six dimensions beyond one loop
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas
• Critical and multicritical Lee-Yang fixed points in the local potential approximation