Nonrelativistic Banks-Casher relation and random matrix theory for multicomponent 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) × SU(N ) → 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 ε-regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.

Exact relations for twist-3 gluon distribution and fragmentation functions from operator identities

“…Here we derive a relation from the nonlocal version of the operator product expansion (OPE) for general correlation functions not necessarily on the lightcone. The method was originally developed in [45,66], and have been frequently used for the twist-3 distributions [24,45,63,67,68], the twist-3 fragmentation functions [59,69], and the distribution amplitudes for hard exclusive processes [66,70,71], etc. This method is equivalent to OPE, and incorporates all the constraints from Lorentz invariance property of the correlation functions.…”

“…Collinear twist-3 DFs and FFs can be in general classified into three types: intrinsic, kinematical and dynamical ones [59] . Although they all appear in the calculation of the twist-3 cross section formula, they are not independent from each other, but are related by QCD equation of motion (e.o.m.)…”

“…performed a systematic study on the twist-3 quark DFs and FFs, and presented a complete set of those model independent relations, which are often called e.o.m. relations and the Lorentz invariance relations (LIR) [59]. These relations allow one to express the intrinsic and kinematical twist-3 DFs and FFs in terms of the twist-2 functions and the dynamical twist-3 functions.…”

“…These relations allow one to express the intrinsic and kinematical twist-3 DFs and FFs in terms of the twist-2 functions and the dynamical twist-3 functions. In addition, they play a critical role to guarantee the gauge invariance and frame independence of the twist-3 cross sections [29,59,60]. In this paper, we extend the study to gluonic twist-3 DFs and FFs for a spin-1/2 hadron [37-39, 61, 62] and derive all of those exact relations.…”

Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model

“…For example, Dirac and Weyl fermions appear in the low-energy effective field theories of graphene, topological insulators, semimetals, and dwave superconductors (see the reviews [16]) which can be combined with the RMT approach to condensed matter and disordered systems [17]. Also nonrelativistic fermions with quadratic dispersion may be described by chiral RMT [18].…”