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Title: 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}
}