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

Kridsanaphong Limtragool, Zhidong Leong, Philip W. Phillips

Research output: Contribution to journalArticlepeer-review


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 ImG(ω = 0, -∞) = 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.

Original languageEnglish (US)
Article number049
JournalSciPost Physics
Issue number5
StatePublished - Nov 2018

ASJC Scopus subject areas

  • General Physics and Astronomy


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