Effective Field Theory for Dilute Fermi Systems

Abstract

The virtues of an effective field theory (EFT) approach to many-body problems are illustrated by deriving the expansion for the energy of an homogeneous, interacting Fermi gas at low density and zero temperature. A renormalization scheme based on dimensional regularization with minimal subtraction leads to a more transparent power-counting procedure and diagrammatic expansion than conventional many-body approaches. Coefficients of terms in the expansion with logarithms of the Fermi momentum are determined by the renormalization properties of the EFT that describes few-body scattering. Lessons for an EFT treatment of nuclear matter are discussed.

19 pages, RevTeX, 4 ps figures, included using epsf.tex, references added, discussion clarified, typo in eq. (5) corrected

References in corpus (5)

• Evaporative Cooling of a Two-Component Degenerate Fermi Gas
• Saturation from nuclear pion dynamics
• What is Renormalization?
• Perturbative Effective Field Theory at Finite Density
• Describing Nuclear Matter with Effective Field Theories

Cited by in corpus (96)

• Modern Theory of Nuclear Forces
• Universality in Few-body Systems with Large Scattering Length
• Effective Field Theory for Few-Nucleon Systems
• Neutron Radii in Mean-Field Models
• Nuclear effective field theory: status and perspectives
• Three-body forces: From cold atoms to nuclei
• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Quantifying truncation errors in effective field theory
• Chiral Dynamics and Nuclear Matter
• Rearranging Pionless Effective Field Theory
• Toward ab initio density functional theory for nuclei
• In-medium chiral perturbation theory beyond the mean-field approximation
• Nuclear chiral dynamics and thermodynamics
• Are Occupation Numbers Observable?
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• T_c for dilute Bose gases: beyond leading order in 1/N
• Nonuniversal Effects in the Homogeneous Bose Gas
• Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry
• Low-Energy Universality in Atomic and Nuclear Physics
• Pion-less effective field theory for atomic nuclei and lattice nuclei
• Many Body Methods and Effective Field Theory
• Ground State Energy of the Low Density Fermi Gas
• Resummation of fermionic in-medium ladder diagrams to all orders
• Density dependence of the nuclear energy-density functional
• An effective field theory for coupled-channel scattering
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• Field Redefinitions at Finite Density
• Effective density functionals beyond mean field
• Nonperturbative Effects on the Ferromagnetic Transition in Repulsive Fermi Gases
• Effective theory for deformed nuclei
• The Kinetic Energy Density in Kohn-Sham Density Functional Theory
• Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction
• From dilute matter to the equilibrium point in the energy--density--functional theory
• Pauli blocking effects and Cooper triples in three-component Fermi gases
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Effective Field Theory and Finite Density Systems
• Dilute resonating gases and the third virial coefficient
• Chiral Lagrangians at finite density
• Density Functional Theory: Methods and Problems
• Effective Field Theory for Dilute Fermions with Pairing
• Theory of SU(N) Fermi liquid
• Effective Field Theory for Fermi Systems in a large N expansion
• Energy-density functionals inspired by effective-field theories: Applications to neutron drops
• Resurgence for superconductors
• From resonantly interacting fermions with effective range to neutron matter
• Cold Atom Quantum Simulator for Dilute Neutron Matter
• A Lee-Yang--inspired functional with a density--dependent neutron-neutron scattering length
• From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter
• Eft for DFT
• Dilute Fermi gas at fourth order in effective field theory
• To which densities is spin-polarized neutron matter a weakly interacting Fermi gas?
• Consequences of kinetic non-equilibrium for the nuclear equation-of-state in heavy ion collision
• Quasiparticle Properties in Effective Field Theory
• Effective field theory for dilute Fermi systems at fourth order
• Single-Particle Properties from Kohn-Sham Green's Functions
• Effective 3-Body Interaction for Mean-Field and Density-Functional Theory
• Uncertainty quantification in electromagnetic observables of nuclei
• Interaction energy and itinerant ferromagnetism in a strongly interacting Fermi gas in the absence of molecule formation
• Rotational constants of multi-phonon bands in an effective theory for deformed nuclei
• Finite range and upper branch effects on itinerant ferromagnetism in repulsive Fermi gases: Bethe-Goldstone ladder resummation approach
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• Third-order particle-hole ring diagrams with contact-interactions and one-pion exchange
• Dimensional regularization applied to nuclear matter with a zero--range interaction
• On-shell approximation for the s-wave scattering theory
• Zero-temperature limit and statistical quasiparticles in many-body perturbation theory
• Lee-Yang-inspired energy-density functional including contributions from $p$-wave scattering
• Single-particle potential from resummed ladder diagrams
• SU(N) Fermi liquid at finite temperature
• Application of an ab-initio-inspired energy density functional to nuclei: impact of the effective mass and the slope of the symmetry energy on bulk and surface properties
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Ground state energy of the polarized diluted gas of interacting spin $1/2$ fermions
• Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis
• Few-Body Route to One-Dimensional Quantum Liquids
• Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
• Effective field theory of pairing rotations
• Coherent collisional decoherence
• Resonant spectra of multipole-bound anions
• Nuclear structure far from stability
• Three-loop Corrections in a Covariant Effective Field Theory
• Renormalization of pionless effective field theory in the A-body sector
• Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes
• Effective Theories of Dense and Very Dense Matter
• Recent Developments in the Nuclear Many-Body Problem
• Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory
• Toward precision Fermi liquid theory in two dimensions
• Renormalization of the Sigma-Omega model within the framework of U(1) gauge symmetry
• Skewness of nuclear matter and three-particle correlations
• Third order corrections to the ground state energy of the gas of spin $s$ fermions with arbitrary densities of different spin projections
• Particle-hole ring diagrams for fermions in two dimensions
• Closed-form Brückner $G$-matrix and nuclear matter in EFT($/\pi$)
• Misconceptions on Effective Field Theories and spontaneous symmetry breaking: Response to Ellis' article
• Local energy density functional for superfluid Fermi gases from effective field theory
• Multicomponent Fermi systems at low densities
• Three-Body Interactions in Many-Body Effective Field Theory