We describe an approach to the theory of the Fermi surface based on the renormalization group. A notion of the quasiparticle appears naturally in the theory. The \ensuremath{\beta} function is finite to all orders of the perturbation theory and we compute and discuss it to second order. The normality of the Fermi surface is linked to the repulsivity of the quasiparticle potential; the remarkable cancellations that occur in the \ensuremath{\beta} function lead one to think that a normal Fermi surface can perhaps occur, but only when the interaction between the quasiparticles is repulsive. The approach was first proposed in an earlier paper and we give an improved version of it here referring to the earlier work only to make use of technical estimates derived there.We describe an approach to the theory of the Fermi surface based on the renormalization group. A notion of the quasiparticle appears naturally in the theory. The \ensuremath{\beta} function is finite to all orders of the perturbation theory and we compute and discuss it to second order. The normality of the Fermi surface is linked to the repulsivity of the quasiparticle potential; the remarkable cancellations that occur in the \ensuremath{\beta} function lead one to think that a normal Fermi surface can perhaps occur, but only when the interaction between the quasiparticles is repulsive. The approach was first proposed in an earlier paper and we give an improved version of it here referring to the earlier work only to make use of technical estimates derived there.

Physical review. B, Condensed matterDec 1, 199099 citations

Fermi Surface Renormalization Group

R. Shankar

WORLD SCIENTIFIC eBooksAug 1, 20240 citations

Anisotropic renormalization-group flow of quasiparticle weight in a two-dimensional electron system with a partially flat Fermi surface

Jun‐ichiro Kishine, Kenji Yonemitsu

Two-loop renormalization-group (RG) analysis for a two-dimensional electron system with a partially flat Fermi surface has been carried out. We found that the RG flow of the quasiparticle weight depends on the location of the electron wave number $\mathit{k}$ on the Fermi surface due to the kinematical restriction to the logarithmically divergent processes in the flat regions of the Fermi surface.Two-loop renormalization-group (RG) analysis for a two-dimensional electron system with a partially flat Fermi surface has been carried out. We found that the RG flow of the quasiparticle weight depends on the location of the electron wave number $\mathit{k}$ on the Fermi surface due to the kinematical restriction to the logarithmically divergent processes in the flat regions of the Fermi surface.

Physical review. B, Condensed matterJun 15, 199912 citations

Fermions and the Fermi surface

Lecture notes in physics. M, MonographsJan 1, 19970 citations

Non-Fermi-liquid aspects of cold and dense QED and QCD: Equilibrium and nonequilibrium

D. Boyanovsky, Hector J. de Vega

We study equilibrium and nonequilibrium aspects of the normal state of cold and dense QCD and QED. The exchange of dynamically screened magnetic gluons (photons) leads to infrared singularities in the fermion propagator for excitations near the Fermi surface and the breakdown of the Fermi liquid description. We implement a resummation of these infrared divergences via the Euclidean renormalization group to obtain the spectral density, dispersion relation, widths, and wave function renormalization for single quasiparticles near the Fermi surface. We find that all features scale with anomalous dimensions: ${\ensuremath{\omega}}_{p}(k)\ensuremath{\propto}|k\ensuremath{-}{k}_{F}{|}^{1/(1\ensuremath{-}2\ensuremath{\lambda})},$ $\ensuremath{\Gamma}(k)\ensuremath{\propto}|k\ensuremath{-}{k}_{F}{|}^{1/(1\ensuremath{-}2\ensuremath{\lambda})};$ ${Z}_{p}(k)\ensuremath{\propto}|k\ensuremath{-}{k}_{F}{|}^{2\ensuremath{\lambda}/(1\ensuremath{-}2\ensuremath{\lambda})}$ with $\ensuremath{\lambda}=\ensuremath{\alpha}/6\ensuremath{\pi}$ for QED, $({\ensuremath{\alpha}}_{s}/6\ensuremath{\pi}{)(N}_{c}^{2}\ensuremath{-}{1)/2N}_{c}$ for QCD with ${N}_{c}$ colors and ${N}_{F}$ flavors. The discontinuity of the quasiparticle distribution at the Fermi surface vanishes. For $k\ensuremath{\approx}{k}_{F}$ we find ${n}_{k\ensuremath{\approx}{k}_{F}}=\mathrm{sin}[\ensuremath{\pi}\ensuremath{\lambda}]/2\ensuremath{\pi}\ensuremath{\lambda}\ensuremath{-}(k\ensuremath{-}{k}_{F})/\ensuremath{\pi}M(1\ensuremath{-}4\ensuremath{\lambda})+\mathcal{O}(k\ensuremath{-}{k}_{F}{)}^{2}$ with $M$ the dynamical screening scale of magnetic gluons (photons). The dynamical renormalization group is implemented to study nonequilibrium relaxation. The amplitude of single quasiparticle states with momentum near the Fermi surface falls off as $|{\ensuremath{\Psi}}_{k\ensuremath{\approx}{k}_{F}}(t)|\ensuremath{\approx}|{\ensuremath{\Psi}}_{k\ensuremath{\approx}{k}_{F}}{(t}_{0})|{e}^{\ensuremath{-}\ensuremath{\Gamma}(k)(t\ensuremath{-}{t}_{0})}[{t}_{0}/t{]}^{2\ensuremath{\lambda}}.$ Thus quasiparticle states with Fermi momentum have zero group velocity and relax with a power law with a coupling-dependent anomalous dimension.We study equilibrium and nonequilibrium aspects of the normal state of cold and dense QCD and QED. The exchange of dynamically screened magnetic gluons (photons) leads to infrared singularities in the fermion propagator for excitations near the Fermi surface and the breakdown of the Fermi liquid description. We implement a resummation of these infrared divergences via the Euclidean renormalization group to obtain the spectral density, dispersion relation, widths, and wave function renormalization for single quasiparticles near the Fermi surface. We find that all features scale with anomalous dimensions: ${\ensuremath{\omega}}_{p}(k)\ensuremath{\propto}|k\ensuremath{-}{k}_{F}{|}^{1/(1\ensuremath{-}2\ensuremath{\lambda})},$ $\ensuremath{\Gamma}(k)\ensuremath{\propto}|k\ensuremath{-}{k}_{F}{|}^{1/(1\ensuremath{-}2\ensuremath{\lambda})};$ ${Z}_{p}(k)\ensuremath{\propto}|k\ensuremath{-}{k}_{F}{|}^{2\ensuremath{\lambda}/(1\ensuremath{-}2\ensuremath{\lambda})}$ with $\ensuremath{\lambda}=\ensuremath{\alpha}/6\ensuremath{\pi}$ for QED, $({\ensuremath{\alpha}}_{s}/6\ensuremath{\pi}{)(N}_{c}^{2}\ensuremath{-}{1)/2N}_{c}$ for QCD with ${N}_{c}$ colors and ${N}_{F}$ flavors. The discontinuity of the quasiparticle distribution at the Fermi surface vanishes. For $k\ensuremath{\approx}{k}_{F}$ we find ${n}_{k\ensuremath{\approx}{k}_{F}}=\mathrm{sin}[\ensuremath{\pi}\ensuremath{\lambda}]/2\ensuremath{\pi}\ensuremath{\lambda}\ensuremath{-}(k\ensuremath{-}{k}_{F})/\ensuremath{\pi}M(1\ensuremath{-}4\ensuremath{\lambda})+\mathcal{O}(k\ensuremath{-}{k}_{F}{)}^{2}$ with $M$ the dynamical screening scale of magnetic gluons (photons). The dynamical renormalization group is implemented to study nonequilibrium relaxation. The amplitude of single quasiparticle states with momentum near the Fermi surface falls off as $|{\ensuremath{\Psi}}_{k\ensuremath{\approx}{k}_{F}}(t)|\ensuremath{\approx}|{\ensuremath{\Psi}}_{k\ensuremath{\approx}{k}_{F}}{(t}_{0})|{e}^{\ensuremath{-}\ensuremath{\Gamma}(k)(t\ensuremath{-}{t}_{0})}[{t}_{0}/t{]}^{2\ensuremath{\lambda}}.$ Thus quasiparticle states with Fermi momentum have zero group velocity and relax with a power law with a coupling-dependent anomalous dimension.

arXiv:hep-ph/0009172Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJan 11, 200141 citations

\mathit{k}

on the Fermi surface due to the kinematical restriction to the logarithmically divergent processes in the flat regions of the Fermi surface.

{N}_{c}

colors and

{N}_{F}

flavors. The discontinuity of the quasiparticle distribution at the Fermi surface vanishes. For $k\ensuremath{\approx}{k}_{F}$ we find ${n}_{k\ensuremath{\approx}{k}_{F}}=\mathrm{sin}[\ensuremath{\pi}\ensuremath{\lambda}]/2\ensuremath{\pi}\ensuremath{\lambda}\ensuremath{-}(k\ensuremath{-}{k}_{F})/\ensuremath{\pi}M(1\ensuremath{-}4\ensuremath{\lambda})+\mathcal{O}(k\ensuremath{-}{k}_{F}{)}^{2}$ with

M

the dynamical screening scale of magnetic gluons (photons). The dynamical renormalization group is implemented to study nonequilibrium relaxation. The amplitude of single quasiparticle states with momentum near the Fermi surface falls off as $|{\ensuremath{\Psi}}_{k\ensuremath{\approx}{k}_{F}}(t)|\ensuremath{\approx}|{\ensuremath{\Psi}}_{k\ensuremath{\approx}{k}_{F}}{(t}_{0})|{e}^{\ensuremath{-}\ensuremath{\Gamma}(k)(t\ensuremath{-}{t}_{0})}[{t}_{0}/t{]}^{2\ensuremath{\lambda}}.$ Thus quasiparticle states with Fermi momentum have zero group velocity and relax with a power law with a coupling-dependent anomalous dimension.