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Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches

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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

Klöckner, C., Kennes, D. M., & Karrasch, C. (2020). Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches. New Journal of Physics, 22(8): 083039. doi:10.1088/1367-2630/ab990d.


Cite as: http://hdl.handle.net/21.11116/0000-0007-0653-5
Abstract
We introduce a method to evaluate the steady-state non-equilibrium Keldysh–Schwinger Green's functions for infinite systems subject to both an electric field and a coupling to reservoirs. The method we present exploits a physical quasi-translation invariance, where a shift by one unit cell leaves the physics invariant if all electronic energies are simultaneously shifted by the magnitude of the electric field. Our framework is straightaway applicable to diagrammatic many-body methods. We discuss two flagship applications, mean-field theories as well as a sophisticated second-order functional renormalization group approach. The latter allows us to push the renormalization-group characterization of phase transitions for lattice fermions into the out-of-equilibrium realm. We exemplify this by studying a model of spinless fermions, which in equilibrium exhibits a Berezinskii–Kosterlitz–Thouless phase transition.