Preservation of sum rules for the 1p-Green function in Luttinger model

J. Kokalj, Peter Prelovšek

靖 小森, 三樹 和達

José Jesús Rodríguez-Núñez, Sandra Schafroth, H Beck

Kridsanaphong Limtragool, Zhidong Leong, Philip Phillips

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 l m G ( 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.

Ivana Mrkonjić, S. Bari ic

J. Kokalj, Peter Prelovšek

The validity of the Luttinger sum rule is considered for finite systems of interacting electrons, where the Fermi volume is determined by location of zeros of Green's function. It is shown that the sum rule in the paramagnetic state is evidently violated within the planar $t\text{\ensuremath{-}}J$ model at low doping while for the related Hubbard model, even in the presence of next-nearest-neighbor hopping, no clear-cut exception is found.