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

作者：Kanazawa Takuya^*; Yamamoto Arata

来源：PHYSICAL REVIEW D, 2016, 93(1): 016010.

DOI：10.1103/PhysRevD.93.016010

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) x SU(N) -> 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 epsilon regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.

• 出版日期2016-1-25
• 单位RIKEN