2015/11/30 by Takuya Kanazawa, Arata Yamamoto
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Degenerate energy levels #Eigenvalues and eigenvectors #Fermion #Mathematical physics #Matrix (chemical analysis) #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Quantum chromodynamics #Quantum many-body systems #Quantum mechanics #Random matrix #Superfluidity #cond-mat.quant-gas #hep-lat #hep-ph
paper · pdf · doi:10.1103/physrevd.93.016010
published as Phys. Rev. D 93, 016010 (2016) · 14 pages, 5 figures
openalex publication_date 2016/01/25 · arxiv created 2016/04/11 · arxiv updated 2016/04/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We apply QCD-inspired techniques to study nonrelativistic N-component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize spontaneous symmetry breaking U(1)\ifmmode×\else\texttimes\fiSU(N)\ensuremath→Sp(N) through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Nonlocal order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived, and its equivalence to random matrix theory is demonstrated in the ϵ regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.