https://doi.org/10.1140/epjb/s10051-022-00445-3
Regular Article - Solid State and Materials
Review of recent developments of the functional renormalization group for systems out of equilibrium
1
Institut für Mathematische Physik, Technische Universität Braunschweig, Mendelssohnstraße 3, 38106, Braunschweig, Germany
2
Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056, Aachen, Germany
3
Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761, Hamburg, Germany
Received:
4
May
2022
Accepted:
20
October
2022
Published online:
2
December
2022
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.
© The Author(s) 2022
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