Growth of instabilities in a normal Fermi liquid

C. J. Pethick, D. G. Ravenhall

Kelly R. Patton, Daniel E. Sheehy

Yiming Pan, Jinze He, Qiaofei Pan

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.

D. ter Haar

Wonjune Choi, Omid Tavakol, Yong Baek Kim

The interplay of non-Fermi liquid and superconductivity born out of strong dynamical interactions is at the heart of the physics of unconventional superconductivity. As a solvable platform of the strongly correlated superconductors, we study the pairing instabilities of the Yukawa-Sachdev-Ye-Kitaev (Yukawa-SYK) model, which describes spin-1/2 fermions coupled to bosons by the random, all-to-all, spin-independent and dependent Yukawa interactions. In contrast to the previously studied models, the random Yukawa couplings are sampled from a collection of Gaussian ensembles whose variances follow a continuous distribution rather than being fixed to a constant. By tuning the analytic behaviour of the distribution, we could control the fermion incoherence to systematically examine various normal states ranging from the Fermi liquid to non-Fermi liquids that are different from the conformal solution of the SYK model with a constant variance. Using the linearised Eliashberg theory, we show that the onset of the unconventional spin-triplet pairing is preferred with the spin-dependent interactions while all pairing channels show instabilities with the spin-independent interactions. Although the interactions shorten the lifetime of the fermions in the non-Fermi liquid, the same interactions also dress the bosons to strengthen the tendency to pair the incoherent fermions. As a consequence, the onset temperature T_c T c of the pairing is enhanced in the non-Fermi liquid compared to the case of the Fermi liquid.

I.Ya. Pomeranchuk