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

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Kennes,  D. M.
Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology;
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Citation

Camacho, G., Klöckner, C., Kennes, D. M., & Karrasch, C. (2022). Review of recent developments of the functional renormalization group for systems out of equilibrium. The European Physical Journal B: Condensend Matter Physics, 95(12): 195. doi:10.1140/epjb/s10051-022-00445-3.


Cite as: https://hdl.handle.net/21.11116/0000-000A-635F-D
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.