Aspects of Renormalization in Finite Density Field Theory

Abstract

We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction "Landau parameters" run already at tree level. Our explicit one loop analysis resolves previously found obstacles in the renormalization of finite density field theory, including logarithmic divergences in non-local interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of $2k_F$ singularities, and a companion paper considers the RG for Fermi surface instabilities. We end with some comments on the renormalization of finite density field theory with the inclusion of Landau damping of the boson.

30 pages plus Appendix. v2: typos corrected, references added

References in corpus (5)

• Are non-Fermi-liquids stable to Cooper pairing?
• A controlled expansion for certain non-Fermi liquid metals
• Quantum critical metals in $4-\epsilon$ dimensions
• Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point
• Enhanced Pairing of Quantum Critical Metals Near d=3+1

Cited by in corpus (9)

• Quantum critical metals in $4-\epsilon$ dimensions
• How non-Fermi liquids cure their infrared divergences
• The special role of the first Matsubara frequency for superconductivity near a quantum-critical point -- the non-linear gap equation below $T_c$ and spectral properties in real frequencies
• Superconductivity of incoherent electrons in Yukawa-SYK model
• Dynamic mass generation and topological order in overscreened Kondo lattices
• Odd frequency pairing in a quantum critical metal
• Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective
• Infinite critical boson induced non-Fermi liquid in $d=3-\epsilon$ dimensions
• Local energy density functional for superfluid Fermi gases from effective field theory