Kridsanaphong Limtragool, Zhidong Leong, Philip W. Phillips
SciPost Phys. 5, 049 (2018) ·
published 16 November 2018

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We investigate the validity of Luttinger's theorem (or Luttinger sum rule) in
two scaleinvariant fermionic models. We find that, in general, Luttinger's
theorem does not hold in a system of fermions with powerlaw Green functions
which do not necessarily preserve particlehole symmetry. However, Ref.
\cite{Blagoev1997,Yamanaka1997} showed that Luttinger liquids, another
scaleinvariant 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: particlehole
symmetry and $\mathrm{Im} G(\omega=0,\infty)=0$. We conjecture that these two
properties represent sufficient, but not necessary, conditions for the validity
of the Luttinger sum rule in condensed matter systems.