Vertex functions at finite momentum: Application to antiferromagnetic quantum criticality

Abstract

We analyze the three-point vertex function that describes the coupling of fermionic particle-hole pairs in a metal to spin or charge fluctuations at non-zero momentum. We consider Ward identities, which connect two-particle vertex functions to the self energy, in the framework of a Hubbard model. These are derived using conservation laws following from local symmetries. The generators considered are the spin density and particle density. It is shown that at certain antiferromagnetic critical points, where the quasiparticle effective mass is diverging, the vertex function describing the coupling of particle-hole pairs to the spin density Fourier component at the antiferromagnetic wavevector is also divergent. Then we give an explicit calculation of the irreducible vertex function for the case of three-dimensional antiferromagnetic fluctuations, and show that it is proportional to the diverging quasiparticle effective mass .

References in corpus (3)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Ultraviolet/infrared mixing in non-Fermi liquids
• Quasi-Local Strange Metal

Cited by in corpus (5)

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• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Strong coupling theory of heavy fermion criticality II
• Superconductivity at an antiferromagnetic quantum critical point: the role of energy fluctuations
• Missing spectral weight in a heavy-fermion system far above Néel temperature