Violation of Luttinger's theorem in the simplest doped Mott insulator: Falicov-Kimball model in strong correlation limit

TL;DR

This paper demonstrates the violation of Luttinger's theorem in the doped Falicov-Kimball model using Monte Carlo simulations, revealing non-Fermi liquid behavior and unconventional Mott transition characteristics in strong correlation regimes.

Contribution

It provides the first unbiased Monte Carlo evidence of Luttinger's theorem violation in the FK model and offers a new understanding of non-Fermi liquid behavior in strongly correlated systems.

Findings

Violation of Luttinger's theorem in FK model confirmed by Monte Carlo.

Identification of Mott insulator-metal transition with unconventional scaling.

Discovery of a two-peak band structure linked to theorem violation.

Abstract

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.