An all-electronic FRG with retarded phonon-mediated interactions treats charge, spin, nematic, and pairing instabilities on equal footing and is illustrated for the square-lattice Hubbard model with acoustic phonons.
Marsiglio, Eliashberg theory: A short review, Annals of Physics Eliashberg Theory at 60: Strong-coupling Su- perconductivity and Beyond,417, 168102 (2020)
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Electron-Phonon Functional Renormalization Group of Fermi Liquid Instabilities
An all-electronic FRG with retarded phonon-mediated interactions treats charge, spin, nematic, and pairing instabilities on equal footing and is illustrated for the square-lattice Hubbard model with acoustic phonons.