Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids

Abstract

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 the spontaneous symmetry breaking U(1)xSU(N)$\to$Sp(N) through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Non-local 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 epsilon-regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.

14 pages, 5 figures

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Cited by in corpus (2)

• Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model
• Dirac spectrum and chiral condensate for QCD at fixed $\theta$-angle