Correspondence between many-body localization and Landau–Fermi liquid of weakly interacting electrons and its normal-state instability in solids

In quantum mechanics, the wavefunction of a free electron intrinsically embodies wave-particle duality, exhibiting wave- and (or) particle-like characteristics upon measurement. In solids, electrons depart from this idealized description; their low-energy excitations are quasiparticles that, within a single-particle perspective, govern material behavior. Here, we present a comparative analysis of the normal states within the many-body localization (MBL) and Landau-Fermi liquid (LFL) frameworks. We propose a phenomenological correspondence between LFL quasiparticles and the local integral of motion (LIOMs) in an MBL phase, which we term the MBL/LFL duality, by analogy to the wave-particle duality of an electron in free space. Within this heuristic framework, we argue that instabilities of an MBL 'normal state' can admit analogues of Fermi-liquid (FL) instabilities, such as LIOM pairing, and we outline both mean-field and renormalization-group perspectives that highlight possible routes to exotic nonequilibrium phases. These results are primarily suggestive: where small-scale numerical illustrations are presented, they serve to exemplify the proposed scenarios rather than constitute exhaustive numerical proof. Finally, our work offers a broader perspective in which MBL may represent not only a stable endpoint but also a setting for normal-state instabilities that parallel those of conventional Fermi liquids. We hope that the MBL/LFL duality can provide a new avenue for understanding exotic nonequilibrium phases that may emerge from the interplay between localization and interaction-driven instabilities.