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

Author

Listed:
  • G. Camacho

    (Technische Universität Braunschweig)

  • C. Klöckner

    (Technische Universität Braunschweig)

  • D. M. Kennes

    (RWTH Aachen University and JARA-Fundamentals of Future Information Technology
    Max Planck Institute for the Structure and Dynamics of Matter)

  • C. Karrasch

    (Technische Universität Braunschweig)

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

Suggested Citation

  • G. Camacho & C. Klöckner & D. M. Kennes & C. Karrasch, 2022. "Review of recent developments of the functional renormalization group for systems out of equilibrium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(12), pages 1-28, December.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:12:d:10.1140_epjb_s10051-022-00445-3
    DOI: 10.1140/epjb/s10051-022-00445-3
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    References listed on IDEAS

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    1. N. Dupuis, 2005. "Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 48(3), pages 319-338, December.
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    Cited by:

    1. Carsten Honerkamp & Dante M. Kennes & Volker Meden & Michael M. Scherer & Ronny Thomale, 2022. "Recent developments in the functional renormalization group approach to correlated electron systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(12), pages 1-3, December.

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