  The Luttinger's theorem has long been taken as the key feature of Landau's
Fermi liquid, which signals the presence of quasiparticles. Here, by the
unbiased Monte Carlo method, violation of Luttinger's theorem is clearly
revealed in the Falicov-Kimball (FK) model, indicating the robust
correlation-driven non-Fermi liquid characteristic under any electron density.
Introducing hole carriers to the half-filled FK leads to Mott insulator-metal
transition, where the Mott quantum criticality manifests unconventional scaling
behavior in transport properties. Further insight on the violation of the
Luttinger's theorem is examined by combining Hubbard-I approximation with a
composite fermion picture, which emphasizes the importance of a mixed
excitation of the itinerant electron and the composite fermion. Interestingly,
when compared FK model with a binary disorder system, it suggests that the
two-peak band structure discovered by Monte Carlo and Hubbard-I approaches is
underlying the violation of Luttinger's theorem.
