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.
Highlights
Unconventional phases of matter play an integral role in condensed matter research and beyond [1]
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
Summary
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Keywords: strongly correlated electrons, functional renormalization group, non-equilibrium phase transitions
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