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 $\left(T\right)$ dependence of the longitudinal and Hall currents naturally emerges in the NFL metal. Our results show good accord with the experiment in ${\mathrm{V}}_{2-y}{\mathrm{O}}_3$ 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.

• Received 23 January 2017

DOI:https://doi.org/10.1103/PhysRevB.97.075133