The validity of the Luttinger sum rule is investigated within the prototype tight-binding model of interacting fermions in one dimension, i.e., the $t\text{\ensuremath{-}}V$ model including the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$, in order to break the particle-hole symmetry. Scaling analysis of finite-system results at half filling reveals evident breakdown of the sum rule in the large gap regime at $V⪢t$ while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.The validity of the Luttinger sum rule is investigated within the prototype tight-binding model of interacting fermions in one dimension, i.e., the $t\text{\ensuremath{-}}V$ model including the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$, in order to break the particle-hole symmetry. Scaling analysis of finite-system results at half filling reveals evident breakdown of the sum rule in the large gap regime at $V⪢t$ while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.

arXiv:0803.4468Physical Review BOct 9, 200810 citations

Generalized hole-particle transformations and spin reflection positivity in multiorbital systems

Mario Cuoco, Canio Noce

We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In particular, we rigorously determine at half-filling and for different regions of the parameter space the spin, orbital, and $\ensuremath{\eta}$ pairing pseudospin of the ground state of generalized two-orbital Hubbard models that include the Hund's rule coupling.We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In particular, we rigorously determine at half-filling and for different regions of the parameter space the spin, orbital, and $\ensuremath{\eta}$ pairing pseudospin of the ground state of generalized two-orbital Hubbard models that include the Hund's rule coupling.

arXiv:cond-mat/0209062Physical review. B, Condensed matterMay 6, 20029 citations

Binding of Holes in the Hubbard Model

Adriana Moreo

Springer proceedings in physicsJan 1, 19910 citations

V⪢t

while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.