Ground-state energy of the polarized dilute gas of interacting spin-1/2 fermions

The effective field theory approach simplifies the perturbative computation of the ground-state energy of the diluted gas of repulsively interacting fermions allowing in the case of the unpolarized system to easily rederive the classic results up to the (k(F)a(0))(2) order (where k(F) is the system's Fermi momentum and a(0) the s-wave scattering length) and (with more labor) to extend it up to the order (k(F)a(0))(4). The analogous expansion of the ground-state energy of the polarized gas of spin 1/2 fermions is known only up to the k(F)a(0) order (where k(F) stands for k(F up arrow) or k(F down arrow)); the order (k(F)a(0))(2) contribution has been computed (analytically) only using a specific (hard-core type) interaction potential. Here we show that the effective field theory method also allows to easily obtain the order (k(F)a(0))(2) correction to the ground state of the polarized gas in a way applicable to all repulsive interactions.

Automated summary

The effective field theory approach simplifies the perturbative computation of the ground-state energy for diluted gas of repulsively interacting fermions, allowing easy derivation of classic results up to higher orders. The expansion of ground state energy for polarized gas of spin 1/2 fermions is known only up to a certain order and has only been computed with a specific interaction potential. The effective field theory method also provides a way to easily obtain corrections to the ground state of polarized gas applicable to all repulsive interactions.