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

G. Camacho (), C. Klöckner, D. M. Kennes and C. Karrasch
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G. Camacho: Technische Universität Braunschweig
C. Klöckner: Technische Universität Braunschweig
D. M. Kennes: RWTH Aachen University and JARA-Fundamentals of Future Information Technology
C. Karrasch: Technische Universität Braunschweig

The European Physical Journal B: Condensed Matter and Complex Systems, 2022, vol. 95, issue 12, 1-28

Abstract: 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

Date: 2022
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DOI: 10.1140/epjb/s10051-022-00445-3

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