# 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 nonlocal 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 k F 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.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1335077

- Report Number(s):
- SLAC-PUB-16758

Journal ID: ISSN 1098-0121; PRBMDO; arXiv:1410.6811

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 19; Journal ID: ISSN 1098-0121

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; General Physics; Theory-HEP; MATSCI

### Citation Formats

```
Fitzpatrick, A. Liam, Torroba, Gonzalo, and Wang, Huajia.
```*Aspects of renormalization in finite-density field theory*. United States: N. p., 2015.
Web. doi:10.1103/PhysRevB.91.195135.

```
Fitzpatrick, A. Liam, Torroba, Gonzalo, & Wang, Huajia.
```*Aspects of renormalization in finite-density field theory*. United States. doi:10.1103/PhysRevB.91.195135.

```
Fitzpatrick, A. Liam, Torroba, Gonzalo, and Wang, Huajia. Tue .
"Aspects of renormalization in finite-density field theory". United States. doi:10.1103/PhysRevB.91.195135. https://www.osti.gov/servlets/purl/1335077.
```

```
@article{osti_1335077,
```

title = {Aspects of renormalization in finite-density field theory},

author = {Fitzpatrick, A. Liam and Torroba, Gonzalo and Wang, Huajia},

abstractNote = {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 nonlocal 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 k F 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.},

doi = {10.1103/PhysRevB.91.195135},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

issn = {1098-0121},

number = 19,

volume = 91,

place = {United States},

year = {2015},

month = {5}

}