Fermi Liquid near a q=0 Charge Quantum Critical Point

Abstract

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 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 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 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 $m^{\ast }$, 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.

13 pages, 8 figures

References in corpus (26)

• Nematic Fermi Fluids in Condensed Matter Physics
• Quantum Theory of a Nematic Fermi Fluid
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Recent Developments in Non-Fermi Liquid Theory
• Perturbative non-Fermi liquids from dimensional regularization
• Large $N$ theory of critical Fermi surfaces
• Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals
• Fermi liquid near Pomeranchuk quantum criticality
• Quasiparticles beyond the Fermi liquid and heavy fermion criticality
• `Local' Quantum Criticality at the Nematic Quantum Phase Transition
• Spin conservation and Fermi liquid near a ferromagnetic quantum critical point
• Spin-triplet superconductivity at the onset of isospin order in biased bilayer graphene
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Normal state properties of quantum critical metals at finite temperature
• Low temperature $T$-linear resistivity due to umklapp scattering from a critical mode
• Non-Landau damping of magnetic excitations in systems with localized and itinerant electrons
• The ladder physics in the Spin Fermion model
• Quasiparticle interaction function in a 2D Fermi liquid near an antiferromagnetic critical point
• Fermi-liquid theory and Pomeranchuk instabilities: fundamentals and new developments
• Quantum criticality in two dimensions and Marginal Fermi Liquid
• Optical conductivity of a metal near an Ising-nematic quantum critical point
• Controlled expansion for transport in a class of non-Fermi liquids
• Gradient terms in quantum-critical theories of itinerant fermions

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