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.

arXiv comment30 pages plus Appendix. v2: typos corrected, references added

References in corpus (22)

• Renormalization Group Approach to Interacting Fermions
• Superconductivity by long-range color magnetic interaction in high-density quark matter
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• On the low energy properies of fermions with singular interactions
• Are non-Fermi-liquids stable to Cooper pairing?
• Low Energy Dynamics of the Spinon-Gauge System
• Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal
• On finite-density QCD at large Nc
• Perturbative non-Fermi liquids from dimensional regularization
• Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Ultraviolet/infrared mixing in non-Fermi liquids
• Non-Fermi Liquid Behaviour, the BRST Identity in the Dense Quark-Gluon Plasma and Color Superconductivity
• A controlled expansion for certain non-Fermi liquid metals
• Non-Fermi Liquid Effects in QCD at High Density
• Quantum critical metals in $d=3+1$
• Quantum critical metals in $4-\epsilon$ dimensions
• Large-density field theory, viscosity, and "$2k_F$" singularities from string duals
• Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point
• Renormalization Group for Mixed Fermion-Boson Systems
• Enhanced Pairing of Quantum Critical Metals Near d=3+1
• Quantum-critical theory of the spin-fermion model and its application to cuprates. Normal state analysis

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