Fermi Liquid near a q=0 Charge Quantum Critical Point
arxiv(2024)
摘要
We analyze the quasiparticle interaction function (the fully dressed and
antisymmetrized interaction between fermions) for a two-dimensional Fermi
liquid at zero temperature close to a q=0 charge quantum critical point (QCP)
in the s-wave channel. By the Ward identities, this vertex function must be
related to quasiparticle residue Z, which can be obtained independently from
the fermionic self-energy. We show that to satisfy these Ward identities, one
needs to go beyond the standard diagrammatic formulation of Fermi liquid theory
and include series of additional contributions to the vertex function. These
contributions are forbidden in a conventional Fermi liquid, but do emerge near
a QCP, where the effective 4-fermion interaction is mediated by a soft
dynamical boson. We demonstrate explicitly that including these terms restores
the Ward identity. We also discuss the role of Aslamazov-Larkin-type diagrams
for the vertex function. Our analysis is built on works on the vertex function
near an antiferromagnetic QCP [Phys. Rev. B 89, 045108 (2014)] and a d-wave
charge-nematic QCP [Phys. Rev. B 81, 045110 (2010)]. We show that for s-wave
charge QCP (the one leading to phase separation), the analysis is more
straightforward. We also discuss the structure of the Landau function in a
critical Fermi liquid near a QCP.
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