Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory

Abstract

In the present work, we start from a minimal Hamiltonian for Fermi systems where the s-wave scattering is the only low energy constant at play. Many-Body Perturbative approach that is usually valid at rather low density is first discussed. We then use the resummation technique with the ladder approximation to obtain compact expressions for both the energy and/or the on-shell self-energy in infinite spin-degenerated systems. Diagrammatic resummation technique has the advantage in general to be predictive in a region of density larger compared to many-body perturbation theory. It also leads to non-diverging limit as $|a_s|\to +\infty$. Still, the obtained expressions are rather complex functional of the Fermi momentum $k_F$. We introduce the full phase-space average or the partial phase-space methods respectively applied to the energy or to the self-energy to simplify their dependences in terms of $(a_s{k}_F)$ while keeping the correct limit at low density and the non-diverging property at large $|a_s{k}_F|$. Quasi-particle properties of Fermi system in various regime of density and scattering length are then illustrated. Our conclusion is that such simplified expressions where the direct link is made with the low energy constant without fine-tuning can provide a clear guidance to obtain density functional theory beyond the perturbative regime. However, quasi-particle properties close or near unitary cannot be reproduced unless this limit is explicitly used as a constraint. We finally discuss how such approximate treatment of quasi-particle can guide the development of density functional theory for strongly interacting Fermi systems.

References in corpus (70)

• Feshbach Resonances in Ultracold Gases
• Cuba - a library for multidimensional numerical integration
• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Observation of quantum droplets in a strongly dipolar Bose gas
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Two-Nucleon Systems from Effective Field Theory
• Using photoemission spectroscopy to probe a strongly interacting Fermi gas
• The Unitary Fermi Gas: From Monte Carlo to Density Functionals
• The Skyrme Interaction in finite nuclei and nuclear matter
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Thermodynamics of the BCS-BEC crossover
• Fermi systems with long scattering lengths
• Quantum Monte Carlo Studies of Superfluid Fermi Gases
• Feynman diagrams versus Fermi-gas Feynman emulator
• Dilute Quantum Droplets
• Strongly paired fermions: Cold atoms and neutron matter
• Spectral Functions and rf Response of Ultracold Fermionic Atoms
• Quantum Monte Carlo Simulations of the BCS-BEC Crossover at Finite Temperature
• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Equation of state of nuclear and neutron matter at third-order in perturbation theory from chiral EFT
• Effective Field Theory for Dilute Fermi Systems
• Resonantly Interacting Fermions In a Box
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Effective pseudopotential for energy density functionals with higher order derivatives
• Nonlinear Schrödinger equation for a superfluid Fermi gas from BCS to Bose crossover
• Non-perturbative methods for a chiral effective field theory of finite density nuclear systems
• Quantum Monte Carlo approaches to nuclear and atomic physics
• Effective-Range Dependence of Resonantly Interacting Fermions
• Systematics of quadrupolar correlation energies
• Many Body Methods and Effective Field Theory
• Lattice Monte Carlo calculations for unitary fermions in a finite box
• Density-functional theory for fermions in the unitary regime
• An improved density matrix expansion for spin-unsaturated nuclei
• Resummation of fermionic in-medium ladder diagrams to all orders
• Convergence of density-matrix expansions for nuclear interactions
• Testing the density matrix expansion against ab initio calculations of trapped neutron drops
• Contact and Momentum Distribution of the Unitary Fermi Gas
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• Static Response of Neutron Matter
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Full optimization and validation
• Effective density functionals beyond mean field
• The Kinetic Energy Density in Kohn-Sham Density Functional Theory
• Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions
• From dilute matter to the equilibrium point in the energy--density--functional theory
• Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction
• Effective Field Theory and Finite Density Systems
• Ab initio and phenomenological studies of the static response of neutron matter
• Energy-density functionals inspired by effective-field theories: Applications to neutron drops
• Fitting N${}^3$LO pseudopotentials through central plus tensor Landau parameters
• Di-neutrons in neutron matter within Brueckner-Hartree-Fock approach
• From resonantly interacting fermions with effective range to neutron matter
• Non-perturbative Extraction of the Effective Mass in 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
• Functional renormalization-group calculation of the equation of state of one-dimensional nuclear matter inspired by the Hohenberg--Kohn theorem
• Projected Quasi-particle Perturbation theory
• Two-body contributions to the effective mass in nuclear effective interactions
• Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian
• Perturbative Effective Field Theory at Finite Density
• Quasiparticle Properties in Effective Field Theory
• Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions
• Static response, collective frequencies and ground state thermodynamical properties of spin saturated two-component cold atoms and neutron matter
• Momentum-resolved spectroscopy of a Fermi liquid
• Incorporating Brueckner-Hartree-Fock correlations in the Density Matrix Expansion approach
• Di-nucleon structures in homogeneous nuclear matter based on two- and three-nucleon interactions
• Third-order particle-hole ring diagrams with contact-interactions and one-pion exchange
• Single-particle potential from resummed ladder diagrams
• Effective interaction approach to the Fermi hard-sphere system
• Transport properties of the Fermi hard-sphere system

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• Effective field theory for dilute Fermi systems at fourth order
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes
• Ultracold spin-balanced fermionic quantum liquids with renormalized $P$-wave interactions
• Local energy density functional for superfluid Fermi gases from effective field theory