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Thursday June, 10 2021
Landau Fermi liquids in disguise
Order by order in perturbation theory one can prove, e.g., in 3D, that the physical electron decay rate, i.e., the imaginary part of self-energy, vanishes quadratically at zero energy. Landau’s theory of Fermi liquids is conventionally derived assuming that such perturbative result continues to hold true beyond perturbation theory, which is nothing but Landau’s assumption of adiabatic continuation. However, that requires an interaction strength within the convergence radius of the perturbation series, if the latter converges at all, which may not be the case of strongly correlated metals, especially close to a Mott transition.
However, it is evident that requiring an infinite lifetime of the physical electrons at zero energy is excessive for quasiparticles to exist. For that, it would suffice requiring that the quasiparticle lifetime diverges, irrespective of whether the physical electron lifetime does or not.
Here, we show that such simple, yet physically sound, change of perspective has huge implications, Specifically, by just assuming a quadratic vanishing of the quasiparticle decay rate at zero energy, we can prove that well defined quasiparticles do exist close to a Luttinger surface, manifold of k-points where the self-energy diverges at zero energy, as well as to a conventional Fermi surface, manifold of k-points where the Green’s function diverges at zero energy. That occurs despite the physical electron pseudo gap at a Luttinger surface. Quasiparticles at a Luttinger surface behave exactly like those at a Fermi surface, e.g., they yield a linear in temperature specific heat, again in spite of the vanishing density of states of physical electrons.
We finally clarify the physical consequences of the above result in a model calculation based on a toy self-energy that uncovers an interesting interplay between Luttinger and Fermi surfaces.
