Realization of a "Two Relaxation Rates" in the Hubbard-Falicov-Kimball Model

TL;DR

This paper demonstrates the emergence of two distinct relaxation rates in the Hubbard-Falicov-Kimball model using DMFT, explaining deviations from single relaxation rate behavior in correlated metals near the Mott transition.

Contribution

It reveals the natural emergence of two relaxation rates in the HFKM beyond a critical FK interaction, supported by analytical analysis and experimental comparison.

Findings

Two relaxation rates govern longitudinal and Hall currents in the non-LFL metal.

The phenomenon appears beyond a critical FK interaction in the HFKM.

Good agreement with experimental observations in V$_{2-y}$O$_3$ near the MIT.

Abstract

A single transport relaxation rate governs the decay of both, longitudinal and Hall currents in Landau Fermi Liquids (LFL). Breakdown of this fundamental feature, first observed in cuprates and subsequently in other three-dimensional correlated systems close to (partial or complete) Mott metal-insulator transitions, played a pivotal role in emergence of a non-Landau Fermi liquid 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 FK interaction, that two distinct relaxation rates governing distinct temperature ($T$) dependence of the longitudinal and Hall currents naturally emerges in the non-LFL metal. We rationalize this surprising finding by an analytical analysis of the structure of charge and spin correlations in the underlying impurity problem, and point out good accord with observations in the famed case of V$_{2-y}$O$_3$ near the MIT.