Review of recent developments of the functional renormalization group for systems out of equilibrium

TL;DR

This paper reviews recent advances in the functional renormalization group method for analyzing steady states of non-equilibrium systems, focusing on fermion chains and including inelastic processes and frequency dependence.

Contribution

It introduces second-order truncation schemes for the FRG that incorporate frequency dependence and inelastic effects, providing a unified review and key physical insights.

Findings

Computed non-equilibrium phase diagram.

Analyzed the fate of the BKT transition.

Reviewed technical derivation of FRG schemes.

Abstract

We recapitulate recent developments of the functional renormalization group (FRG) approach to the steady state of systems out of thermal equilibrium. In particular, we discuss second-order truncation schemes which account for the frequency-dependence of the two particle vertex and which incorporate inelastic processes. Our focus is on two different types of one-dimensional fermion chains: i) infinite, open systems which feature a translation symmetry, and ii) finite systems coupled to left and right reservoirs. In addition to giving a detailed and unified review of the technical derivation of the FRG schemes, we briefly summarize some of the key physical results. In particular, we compute the non-equilibrium phase diagram and analyze the fate of the Berezinskii-Kosterlitz-Thouless transition in the infinite, open system.