Nonrelativistic Banks-Casher relation and random matrix theory for multicomponent fermionic superfluids
Year: 2016
Type: article
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 spontaneous symmetry breaking $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(N)\ensuremath{\rightarrow}\mathrm{Sp}(N)$ 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.
Authors: Takuya Kanazawa, Arata Yamamoto
Institutions: RIKEN, The University of Tokyo
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2148674677