Transverse Transport, Optical Response and Two Relaxation Rates of $t-J$ Model in $\infty$ Dimensions*

Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field
theory, we compute transverse transport coefficients, the Hall constants, Hall angles, and longitudinal and transverse optical response of the $U=\infty$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller correlated Fermi liquid (GCFL) and the Gutzwiller correlated strange metal (GCSM). We find that the Hall angle $\cot \theta_H$ exhibits a kink that has been seen experimentally but has escaped being commented upon earlier. It is found that $\cot \theta_H \propto T^2$ in GCFL regime, and then shows a downward bend into GCSM regime. Drude peaks are found for both the optical conductivity and the optical Hall angles below certain characteristic energy scales. By comparing the relaxation rates extracted from fitting to the Drude formula, we find that in the GCFL regime there is a single relaxation rate controlling both longitudinal and transverse transport, while in the GCSM regime two different relaxation rates emerge. We trace the origin of this behavior to the dynamical particle-hole asymmetry of the Dyson self-energy, arguably a generic feature of doped Mott insulators.