Optical conductivity of the Hubbard model at finite temperature

TL;DR

This study calculates the optical conductivity and resistivity of the 2D Hubbard model at finite temperature, revealing features consistent with experimental observations in high-Tc superconductors.

Contribution

It provides a finite-temperature analysis of optical conductivity in the Hubbard model using exact diagonalization, connecting theoretical results with experimental data.

Findings

Resistivity is approximately linear in temperature at large U/t and T.

Optical conductivity shows charge excitations, a MIR band, and a Drude peak.

Conductivity decays slower than 1/ω² near the insulator gap.

Abstract

The optical conductivity, $\sigma(\omega)$, of the two dimensional one-band Hubbard model is calculated at finite temperature using exact diagonalization techniques on finite clusters. The in-plane d.c. resistivity, $\rho_{ab}$, is also evaluated. We find that at large U/t and temperature T, $\rho_{ab}$ is approximately linear with temperature, in reasonable agreement with experiments on high-T$_c$ superconductors. Moreover, we note that $\sigma(\omega)$ displays charge excitations, a mid-infrared (MIR) band and a Drude peak, also as observed experimentally. The combination of the Drude peak and the MIR oscillator strengths leads to a conductivity that decays slower than $1/\omega^2$ at energies smaller than the insulator gap near half-filling.