Ward identities for strongly coupled Eliashberg theories

Abstract

We discuss Ward identities for strongly interacting fermion systems described by Eliashberg-type theories. We show that Ward identities are not in conflict with Migdal theorem. We derive diagrammatically Ward identity for a charge vertex in a Fermi liquid, and when a Fermi liquid is destroyed at quantum criticality. We argue that Ward identity for a spin vertex cannot be obtained within Eliashberg theory.

7 pages, 4 figures

References in corpus (3)

• Quantum-critical behavior of itinerant ferromagnets
• Density Fluctuation Mediated Superconductivity
• Breakup of a Stoner model for the 2D ferromagnetic quantum critical point

Cited by in corpus (24)

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• Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
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• Quasiparticle interaction function in a 2D Fermi liquid near an antiferromagnetic critical point
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• Luttinger-Ward functional approach in the Eliashberg framework : A systematic derivation of scaling for thermodynamics near a quantum critical point
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study
• A theory of criticality for quantum ferroelectric metals
• Collective density fluctuations of strange metals with critical Fermi surfaces
• Vertex correction and Ward identity in the U(1) gauge theory with Fermi surface
• Vertex corrections of impurity scattering at a ferromagnetic quantum critical point
• Fermionization for charge degrees of freedom and bosonization of spin degrees of freedom in the SU(2) slave-boson theory
• Interaction-mitigated Landau damping
• Spin pumping effect in non-Fermi liquid metals
• Superconductivity from a non-Fermi liquid metal : Kondo fluctuation mechanism in the slave-fermion theory
• Ward identity preserving approach for investigation of phonon spectrum with self-energy and vertex corrections