# A Strange Metal from Gutzwiller correlations in infinite dimensions II: Transverse Transport, Optical Response and Rise of Two Relaxation Rates

## TL;DR

This paper investigates the transverse transport and optical properties of the infinite-dimensional Hubbard model using two theoretical approaches, revealing a transition from a single to dual relaxation rates across different correlated regimes.

## Contribution

It introduces a detailed analysis of transport and optical responses in strongly correlated systems, highlighting the emergence of two relaxation rates in the strange metal regime.

## Key findings

- Hall angle $ heta_H$ follows $T^2$ in the Fermi liquid regime
- Weak temperature dependence of $R_H$ in Fermi liquid, strong in strange metal
- Transition from one to two relaxation rates across regimes

## Abstract

Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field theory, we compute the transverse transport coefficients, namely the Hall constants $R_H$ and Hall angles $\theta_H$, and also the 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 angles $\cot \theta_H \propto T^2$ in the GCFL regime, on warming into the strange metal regime, it passes through a downward bend and continues as $T^2$. Equivalently, $R_H$ is weakly temperature dependent in the GCFL regime, and becomes strongly $T$-dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity $\sigma_{xx}(\omega)$ and the optical Hall angles $\tan \theta_H(\omega)$ 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 independent 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.