Abstract
The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral IL, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of IL with IL = ±π/2, occur in impurity models classified as singular Fermi liquids. Here we show the same values, IL = ±π/2, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.
Highlights
The characteristic feature of a Fermi liquid is that the low energy behavior can be understood in terms of interacting quasiparticles and their collective excitations
The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral IL, which is the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons
It is known that non-zero values of IL with IL = ±π/2, occur in impurity models in phases with non-analytic low energy scattering, classified as singular Fermi liquids
Summary
The characteristic feature of a Fermi liquid is that the low energy behavior can be understood in terms of interacting quasiparticles and their collective excitations. It is known that non-zero values of IL with IL = ±π/2, occur in impurity models in phases with non-analytic low energy scattering, classified as singular Fermi liquids.
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