Realization of a scenario with two relaxation rates in the Hubbard Falicov-Kimball model

Abstract

A single transport relaxation rate governs the decay of both longitudinal and Hall currents in Landau Fermi liquids (FL). Breakdown of this fundamental feature, first observed in two-dimensional cuprates and subsequently in other three-dimensional correlated systems close to the Mott metal-insulator transition, played a pivotal role in emergence of a non-FL (NFL) paradigm in higher dimensions $D(>1)$. Motivated hereby, we explore the emergence of this ``two relaxation rates'' scenario in the Hubbard Falicov-Kimball model (HFKM) using the dynamical mean-field theory (DMFT). Specializing to $D=3$, we find, beyond a critical Falicov-Kimball (FK) interaction, that two distinct relaxation rates governing distinct temperature $(T)$ dependence of the longitudinal and Hall currents naturally emerges in the NFL metal. Our results show good accord with the experiment in ${\mathrm{V}}_{2\ensuremath{-}y}{\mathrm{O}}_{3}$ near the metal-to-insulator transition (MIT). We rationalize this surprising finding by an analytical analysis of the structure of charge and spin Hamiltonians in the underlying impurity problem, specifically through a bosonization method applied to the Wolff model and connecting it to the x-ray edge problem.