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 (the one leading to phase separation). 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 a series of additional contributions to the vertex function. These contributions are not present 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. Our analysis is built on previous studies of the vertex function near an antiferromag netic QCP [Phys. Rev. B 89, 045108 (2014)] and a 𝑑-wave charge-nematic QCP [Phys. Rev. B 81, 045110 (2010)]. We show th at for 𝑠−wave charge QCP the analysis is more straightforward and allows one to obtain the full quasiparticle interaction function (the Landau function) near a QCP. We show that all partial components of this function (Landau parameters) diverge near a QCP, in the same way as the effective mass 𝑚*, except for the 𝑠-wave charge component, which approaches −1. Consequently, the susceptibilities in all channels, except for the critical one, remain finite at a QCP, as they should.

中文翻译：

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aq=0 电荷量子临界点附近的费米液体


我们分析了二维费米液体在零温度下接近 s-wave 通道（导致相分离的那个）中 q=0 电荷量子临界点 （QCP） 的准粒子相互作用函数（费米子之间的完全修饰和反对称相互作用）。根据 Ward 恒等式，这个顶点函数必须与准粒子残基 Z 相关，它可以独立于费米子自能获得。我们表明，为了满足这些 Ward 恒等式，需要超越费米液体理论的标准图解公式，并包括一系列对顶点函数的额外贡献。这些贡献不存在于传统的费米液体中，但确实出现在 QCP 附近，其中有效的 4-费米子相互作用是由软动力学玻色子介导的。我们明确证明，包含这些术语可以恢复 Ward 的身份。我们的分析建立在先前对反铁磁磁离子 QCP [Phys. Rev. B89， 045108 （2014）] 和 d 波电荷向列 QCP [Phys. Rev. B81， 045110 （2010）] 附近的顶点函数的研究之上。我们展示了 th at 对于 s-wave 电荷 QCP，分析更直接，并允许在 QCP 附近获得完整的准粒子相互作用函数（朗道函数）。我们表明，该函数的所有部分分量（Landau 参数）在 QCP 附近发散，其方式与有效质量 m* 相同，但 s 波电荷分量除外，它接近 −1。 因此，除关键通道外，所有通道的敏感性在 QCP 中都保持有限，正如它们应该的那样。