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 leaves th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2020-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab990d |
| _version_ | 1797750415385690112 |
|---|---|
| author | C Klöckner D M Kennes C Karrasch |
| author_facet | C Klöckner D M Kennes C Karrasch |
| author_sort | C Klöckner |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:33:26Z |
| format | Article |
| id | doaj.art-62ac2cf2cf724e4fa3129e3211478778 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:33:26Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-62ac2cf2cf724e4fa3129e32114787782023-08-08T15:24:11ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122808303910.1088/1367-2630/ab990dPhases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approachesC Klöckner0D M Kennes1C Karrasch2Technische Universität Braunschweig, Institut für Mathematische Physik , Mendelssohnstraße 3, 38106 Braunschweig, GermanyInstitut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology , 52056 Aachen, Germany; Max Planck Institute for the Structure and Dynamics of Matter , Luruper Chaussee 149, 22761 Hamburg, GermanyTechnische Universität Braunschweig, Institut für Mathematische Physik , Mendelssohnstraße 3, 38106 Braunschweig, GermanyWe 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.https://doi.org/10.1088/1367-2630/ab990dstrongly correlated electronsfunctional renormalization groupnon-equilibrium phase transitions |
| spellingShingle | C Klöckner D M Kennes C Karrasch Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches New Journal of Physics strongly correlated electrons functional renormalization group non-equilibrium phase transitions |
| title | Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches |
| title_full | Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches |
| title_fullStr | Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches |
| title_full_unstemmed | Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches |
| title_short | Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches |
| title_sort | phases of translation invariant systems out of equilibrium iterative green s function techniques and renormalization group approaches |
| topic | strongly correlated electrons functional renormalization group non-equilibrium phase transitions |
| url | https://doi.org/10.1088/1367-2630/ab990d |
| work_keys_str_mv | AT cklockner phasesoftranslationinvariantsystemsoutofequilibriumiterativegreensfunctiontechniquesandrenormalizationgroupapproaches AT dmkennes phasesoftranslationinvariantsystemsoutofequilibriumiterativegreensfunctiontechniquesandrenormalizationgroupapproaches AT ckarrasch phasesoftranslationinvariantsystemsoutofequilibriumiterativegreensfunctiontechniquesandrenormalizationgroupapproaches |