Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:math-ph/0209043 · Reviews in Mathematical Physics

SINGLE SCALE ANALYSIS OF MANY FERMION SYSTEMS PART 2: THE FIRST SCALE

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

Published Nov 1, 2003• 11 citations
arXivHTMLPDF

Abstract

The first renormalization group map arising from the momentum space decomposition of a weakly coupled system of fermions at temperature zero differs from all subsequent maps. Namely, the component of momentum dual to temperature may be arbitrarily large — there is no ultraviolet cutoff. The methods of Part 1 are supplemented to control this special case.

DOI
10.1142/s0129055x03001783

Related papers

SINGLE SCALE ANALYSIS OF MANY FERMION SYSTEMS PART 3: SECTORIZED NORMS

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

The generic renormalization group map associated to a weakly coupled system of fermions at temperature zero is treated by supplementing the methods of Part 1. The interplay between position and momentum space is captured by "sectors". It is shown that the difference between the complete four-legged vertex and its "ladder" part is irrelevant for the sequence of renormalization group maps.

arXiv:math-ph/0209041•Reviews in Mathematical Physics•Nov 1, 2003•13 citations

SINGLE SCALE ANALYSIS OF MANY FERMION SYSTEMS PART 4: SECTOR COUNTING

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

For a two-dimensional, weakly coupled system of fermions at temperature zero, one principal ingredient used to control the composition of the associated renormalization group maps is the careful counting of the number of quartets of sectors that are consistent with conservation of momentum. A similar counting argument is made to show that particle–particle ladders are irrelevant in the case of an asymmetric Fermi curve.

arXiv:math-ph/0209040•Reviews in Mathematical Physics•Nov 1, 2003•8 citations

Renormalization Group Technique for Quasi-One-Dimensional Interacting Fermion Systems at Finite Temperature

C. Bourbonnais, Benoit Guay, Rachel Wortis

arXiv:cond-mat/0204163•Springer eBooks•May 8, 2006•7 citations

SINGLE SCALE ANALYSIS OF MANY FERMION SYSTEMS PART 1: INSULATORS

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

We construct, using fermionic functional integrals, thermodynamic Green's functions for a weakly coupled fermion gas whose Fermi energy lies in a gap. Estimates on the Green's functions are obtained that are characteristic of the size of the gap. This prepares the way for the analysis of single scale renormalization group maps for a system of fermions at temperature zero without a gap.

Reviews in Mathematical Physics•Nov 1, 2003•15 citations

The temperature zero limit

Joel Feldman, Horst Knörrer, Manfred Salmhofer B +1 more

We prove that, for a broad class of many--fermion models, the amplitudes of renormalized Feynman diagrams converge to their temperature zero values in the limit as the temperature tends to zero.

Journal of Statistical Physics•Jan 1, 1998•11 citations

Renormalization group for mixed fermion-boson systems

Seiji J. Yamamoto, Qimiao Si A

We formulate a momentum-shell renormalization-group (RG) procedure that can be used in theories containing both bosons and fermions with a Fermi surface. We focus on boson-fermion couplings that are nearly forward scattering, i.e., involving small momentum transfer $(\stackrel{P\vec}{q}\ensuremath{\approx}0)$ for the fermions. Special consideration is given to phase space constraints that result from the conservation of momentum and the imposition of ultraviolet cutoffs. For problems where the energy and momentum scale similarly (dynamic exponent $z=1$), we show that more than one formalism can be used and they give equivalent results. When the energy and momentum must scale differently $(z\ensuremath{\ne}1)$, the procedures available are more limited but a consistent RG scheme can still be formulated. The approach is applicable to a variety of problems, such as itinerant-electron magnets and gauge fields interacting with fermions.

arXiv:0906.0014•Physical Review B•May 7, 2010•20 citations
The first renormalization group map arising from the momentum space decomposition of a weakly coupled system of fermions at temperature zero differs from all subsequent maps. Namely, the component of momentum dual to temperature may be arbitrarily large — there is no ultraviolet cutoff. The methods of Part 1 are supplemented to control this special case.
We formulate a momentum-shell renormalization-group (RG) procedure that can be used in theories containing both bosons and fermions with a Fermi surface. We focus on boson-fermion couplings that are nearly forward scattering, i.e., involving small momentum transfer $(\stackrel{P\vec}{q}\ensuremath{\approx}0)$ for the fermions. Special consideration is given to phase space constraints that result from the conservation of momentum and the imposition of ultraviolet cutoffs. For problems where the energy and momentum scale similarly (dynamic exponent z=1z=1z=1), we show that more than one formalism can be used and they give equivalent results. When the energy and momentum must scale differently $(z\ensuremath{\ne}1)$, the procedures available are more limited but a consistent RG scheme can still be formulated. The approach is applicable to a variety of problems, such as itinerant-electron magnets and gauge fields interacting with fermions.