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      Absence of Luttinger's theorem for fermions with power-law Green functions

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      SciPost Physics
      Stichting SciPost

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          Abstract

          We investigate the validity of Luttinger’s theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger’s theorem does not hold in a system of fermions with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. [1,2] showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger’s theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and lmG(\omega=0,-\infty)=0 . We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems.

          Most cited references24

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          'Luttinger liquid theory' of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas

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            Ground-State Energy of a Many-Fermion System. II

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              • Abstract: not found
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              Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions

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                Author and article information

                Journal
                SciPost Physics
                SciPost Phys.
                Stichting SciPost
                2018
                November 16 2018
                : 5
                : 5
                Affiliations
                [1 ]University of Illinois at Urbana Champaign
                Article
                10.21468/SciPostPhys.5.5.049
                805317cb-0b3e-4fc4-8b56-ba43889df8a7
                © 2018

                This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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                Physics
                Physics

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