A Monte Carlo framework is developed to compute the optical conductivity ${\sigma }^{xx}\left(\omega \right)$ and the Hall conductivity ${\sigma }^{xy}\left(\omega \right)$ of the spin-fermion model with thermally fluctuating local moment and is applied to study the non-Fermi-liquid transport behavior of the cuprate superconductors. Both ${\sigma }^{xx}\left(\omega \right)$ and ${\sigma }^{xy}\left(\omega \right)$ calculated are found to exhibit a two-component structure, with a Drude component at low energy and a midinfrared component at higher energy. We find that these two components can be understood as the remnants of the corresponding spectral features contributed by the intraband and interband transition in an antiferromagnetic ordered state, in which the electron band is split into the upper and the lower SDW band. For our choice of parameters, both the Drude and the midinfrared component in $\mathrm{Im}{\sigma }^{xy}\left(\omega \right)$ are found to be positive and there are two sign changes between them. We find that such sign changes can be taken as the precursor of the Fermi surface reconstruction or, more specifically, the emergence of electron pocket in the antiferromagnetic ordered state. Depending on the relative importance of the hole pocket and the electron pocket on the reconstructed Fermi surface and the coupling strength to the local moment, the Drude component in $\mathrm{Im}{\sigma }^{xy}\left(\omega \right)$ can be either positive or negative. These results imply that the Hall response in the low-frequency limit is rather subtle and may depend sensitively on the details of the low-energy physics of the system.

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• Electrical conductivity
• Hall effect
• Optical conductivity
• Spin dynamics
• High-temperature superconductors
• Mott insulators
• Effective field theory
• Hubbard model
• Monte Carlo methods
• Non-Fermi-liquid theory
• Path integrals