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- W2753362328 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>l</mml:mi><mml:mi>m</mml:mi><mml:mi>G</mml:mi><mml:mo stretchy=false form=prefix>(</mml:mo><mml:mi>ω</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>−</mml:mo><mml:mi>∞</mml:mi><mml:mo stretchy=false form=postfix>)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> . We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems." @default.
- W2753362328 created "2017-09-15" @default.
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- W2753362328 date "2018-11-16" @default.
- W2753362328 modified "2023-09-27" @default.
- W2753362328 title "Absence of Luttinger's theorem for fermions with power-law Green functions" @default.
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- W2753362328 doi "https://doi.org/10.21468/scipostphys.5.5.049" @default.
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