Categorical classification of non-Fermi liquids in 2+1 dimensions

Abstract

A defining feature of non-Fermi liquids is a lack of the quasiparticle peak on the Fermi surface in the spectral function, which is usually realized by coupling a finite density of fermions with critical collective fluctuations. However, these features of the two- and three-point vertex functions are qualitatively the same across many non-Fermi liquids, which has made it difficult to classify them beyond the definition by negation. We point out that the four-point function in the pairing channel contains rich information that positively differentiates distinct types of non-Fermi liquids. Using the generalized notion of fixed points that captures scale-dependent universal pairing interaction, we provide a non-perturbative classification of 2+1-dimensional non-Fermi liquids. In the large Fermi momentum limit with fixed dimensionless couplings, metals coupled with long-wavelength critical fluctuations are classified into seven superuniversality classes. Each of them exhibits a unique phase diagram in the space of temperature and bare four-fermion coupling. The present work generalizes the earlier perturbative classification to strongly interacting non-Fermi liquids by leveraging kinematic constraints.