Aspects of renormalization in finite-density field theory

ANDREW LIAM FITZPATRICK; GONZALO TORROBA; HUAJIA WANG

PHYSICAL REVIEW B

AMER PHYSICAL SOC

Lugar: New York; Año: 2015 vol. 91 p. 1 - 16

1098-0121

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 2 kF singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite density field theory with the inclusion of Landau damping of the boson.