Validity of the scattering length approximation in strongly interacting Fermi systems

Abstract

We investigate the energy spectrum of systems of two, three and four spin-1/2 fermions with short range attractive interactions both exactly, and within the scattering length approximation. The formation of molecular bound states and the ferromagnetic transition of the excited scattering state are examined systematically as a function of the 2-body scattering length. Identification of the upper branch (scattering states) is discussed and a general approach valid for systems with many particles is given. We show that an adiabatic ferromagnetic transition occurs, but at a critical transition point kF a much higher than predicted from previous calculations, almost all of which use the scattering length approximation. In the 4-particle system the discrepancy is a factor of 2. The exact critical interaction strength calculated in the 4-particle system is consistent with that reported by experiment. To make comparisons with the adiabatic transition, we study the quench dynamics of the pairing instability using the eigenstate wavefunctions.

7 pages, 7 figures

References in corpus (7)

• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Itinerant ferromagnetism of a repulsive atomic Fermi gas: a quantum Monte Carlo study
• Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances
• Correlated versus Ferromagnetic State in Repulsively Interacting Two-Component Fermi Gases
• Spin fluctuations, susceptibility and the dipole oscillation of a nearly ferromagnetic Fermi gas
• Itinerant ferromagnetism in a Fermi gas with contact interaction: Magnetic properties in a dilute Hubbard model

Cited by in corpus (7)

• The Nature and Properties of a Repulsive Fermi Gas in the "Upper Branch"
• Nonperturbative Effects on the Ferromagnetic Transition in Repulsive Fermi Gases
• Ferromagnetic transition of a two-component Fermi gas of Hard Spheres
• Spin segregation via dynamically induced long-range interaction in a system of ultracold fermions
• Pseudopotential for the 2D contact interaction
• Finite range and upper branch effects on itinerant ferromagnetism in repulsive Fermi gases: Bethe-Goldstone ladder resummation approach
• Dynamical spin-flip susceptibility for a strongly interacting ultracold Fermi gas