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Third-order corrections to the ground-state energy of the gas of spin- fermions with arbitrary densities of different spin projections
Phys. Rev. A 107, 063311 – Published 21 June, 2023
DOI: https://doi.org/10.1103/PhysRevA.107.063311
Abstract
Recently, we computed third-order corrections to the ground-state energy of an arbitrarily polarized diluted gas of spin- fermions interacting through a spin-independent repulsive two-body potential. Here we extend this result to the gas of spin- fermions [a system whose Hamiltonian has an accidental symmetry] with arbitrary densities of fermions having different spin projections. The corrections are computed semianalytically using the effective-field-theory approach and are parametrized by the - and -wave scattering lengths and and the -wave effective radius , measurable in the low-energy fermion-fermion elastic scattering. The result is used to study the impact the higher-order corrections can have on the characteristics of the phase transition (at zero temperature) to the ordered phase (on the emergence of the itinerant ferromagnetism).
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