[Submitted on 24 Jun 2026] (cross-list from cond-mat.quant-gas)
The odd fermion at the edge: odd-even staggering in the trapped, unitary Fermi gas
Silas R. Beane · Domenico Orlando · Susanne Reffert
We investigate the odd-even staggering in the harmonically-trapped unitary Fermi gas at large particle-number charge . Using both a large- BdG description and a complementary large-charge EFT method, we show that for odd particle number the extra fermion forms an edge-localized quasiparticle near the Thomas-Fermi surface rather than a bulk excitation. In the edge limit, the microscopic BdG problem reduces to a universal coupled Airy system whose lowest positive eigenvalue fixes the leading odd-even splitting energy, where is the Bertsch parameter, and is a universal edge coefficient. The associated EFT describes a fermionic mode confined to the boundary and coupled to the superfluid Goldstone field, reproducing the same scaling while introducing a dependence on two low-energy constants. Finally, we numerically compute the spectrum and confirm the predicted scaling and localization properties.
- Comments:
- 31 pages, 7 figures
- Subjects:
- Quantum Gases (cond-mat.quant-gas); High Energy Physics — Theory (hep-th); Nuclear Theory (nucl-th)
- arXiv:
- 2606.26225 [pdf]