Ground state energy of the polarized diluted gas of interacting spin $1/2$ fermions

Abstract

The effective field theory approach simplifies the perturbative computation of the ground state energy of the diluted gas of fermions allowing in the case of the unpolarized system to easily re-derive the classic results up to the $(k_{\mathrm{F}}{a}_0{)}^2$ order (where $k_{\mathrm{F}}$ is the system's Fermi momentum and $a_0$ the $s$-wave scattering length) and (with more labour) to extend it up to the order $(k_{\mathrm{F}}{a}_0{)}^4$. The corresponding expansion of the ground state energy of the polarized gas of spin $1/2$ fermions is known analytically (to our best knowledge) only up to the $k_{\mathrm{F}}{a}_0$ (where $k_{\mathrm{F}}$ stands for $k_{\mathrm{F}\uparrow }$ or $k_{\mathrm{F}\downarrow }$) order. Here we show that the same effective field theory method allows to easily compute also the order $(k_{\mathrm{F}}{a}_0{)}^2$ correction to this result.

arXiv comment24 pages; in the present version, some new remarks are added

References in corpus (19)

• Nuclear effective field theory: status and perspectives
• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Itinerant ferromagnetism of a repulsive atomic Fermi gas: a quantum Monte Carlo study
• Itinerant Ferromagnetism in an Ultracold Atom Fermi Gas
• Correlations and Pair Formation in a Repulsively Interacting Fermi Gas
• Effective Field Theory for Dilute Fermi Systems
• Are Occupation Numbers Observable?
• Ground State Energy of the Low Density Fermi Gas
• Resummation of fermionic in-medium ladder diagrams to all orders
• Compressibility of an Ultracold Fermi Gas with Repulsive Interactions
• Field Redefinitions at Finite Density
• Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: a Quantum Monte Carlo Study
• Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction
• The dilute Fermi gas via Bogoliubov theory
• Dilute Fermi gas at fourth order in effective field theory
• Zero-Temperature Equation of State and Phase Diagram of Repulsive Fermionic Mixtures
• Ground state energy of the low density Hubbard model. An upper bound
• Third-order particle-hole ring diagrams with contact-interactions and one-pion exchange
• Ground state energy of the low density Hubbard model

Cited by in corpus (5)

• Quantum Monte Carlo study of the role of p-wave interactions in ultracold repulsive Fermi gases
• Beyond universality in repulsive SU(N) Fermi gases
• Third order corrections to the ground state energy of the gas of spin $s$ fermions with arbitrary densities of different spin projections
• The Huang-Yang formula for the low-density Fermi gas: upper bound
• Multicomponent Fermi systems at low densities