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

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. Graphic abstract

Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level

“…The FRG is nowadays applied to a broad variety of models in condensed-matter theory, including interacting zero-and one-dimensional fermionic models for quantum dots and wires [8,17]. For some of these applications, the applied approximations are known to reproduce correctly the leading scaling behaviour, which is not accessible by finite order perturbation theory.…”

Recent developments in the functional renormalization group approach to correlated electron systems

“…Camacho et al review the recent efforts in that direction with a focus on one-dimensional fermion chains in Ref. [14] where they also discuss relevant physical applications of these technical developments.…”