Dominic Else - Non-Fermi liquids as ersatz Fermi liquids

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Dominic Else (MIT), "Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals" (7 Aug 2020)
Abstract: A well-known property of Fermi liquids is that have they have a Fermi surface in momentum space whose volume enclosed is determined by the microscopic electron density according to Luttinger's theorem. The situation for metallic states not described by Fermi liquid theory -- so-called "non-Fermi liquids" -- has so far been far less clear. Do these systems necessarily have Fermi surfaces? What exactly do we even mean by a Fermi surface in systems without quasiparticles? If there is a Fermi surface, does it obey Luttinger's theorem?

In this talk, I will describe a recent work [1] in which powerful non- perturbative methods (involving ideas previously appearing in the theory of symmetry-protected topological phases) are applied to these and other related questions. Our results can be viewed as a vast generalization of both Luttinger's theorem and the Lieb-Schultz-Mattis theorem. Along the way, I will introduce the concept of an "ersatz Fermi liquid". For reasons that I will outline, it is to be expected that most if not all non-Fermi liquids are in fact ersatz Fermi liquids. We show that ersatz Fermi liquids share a number of key properties in common with Fermi liquids, including a well-defined Fermi surface that obeys Luttinger's theorem.

[1] https://arxiv.org/abs/2007.07896

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