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

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 leav...

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Bibliographic Details
Published in:New journal of physics 2020-08, Vol.22 (8), p.83039
Main Authors: Klöckner, C, Kennes, D M, Karrasch, C
Format: Article
Language:English
Subjects:
Electric fields
Fermions
functional renormalization group
Invariants
Iterative methods
non-equilibrium phase transitions
Phase transitions
Physics
strongly correlated electrons
Unit cell
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Summary: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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ab990d