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Using determinant Quantum Monte Carlo, we compare three methods of evaluatingthe dc Hall coefficient $R_H$ of the Hubbard model: the direct measurement ofthe off-diagonal current-current correlator $\chi_{xy}$ in a system coupled toa finite magnetic field (FF), $\chi_{xy}^{\text{FF}}$; the three-current linearresponse to an infinitesimal field as measured in the zero-field (ZF) HubbardHamiltonian, $\chi_{xy}^{\text{ZF}}$; and the leading order of the recurrentexpansion $R_H^{(0)}$ in terms of thermodynamic susceptibilities. The twoquantities $\chi_{xy}^{\text{FF}}$ and $\chi_{xy}^{\text{ZF}}$ can be compareddirectly in imaginary time. Proxies for $R_H$ constructed from thethree-current correlator $\chi_{xy}^{\text{ZF}}$ can be determined underdifferent simplifying assumptions and compared with $R_H^{(0)}$. We find thesedifferent quantities to be consistent with one another, validating previousconclusions about the close correspondence between Fermi surface topology andthe sign of $R_H$, even for strongly correlated systems. These variousquantities also provide a useful set of numerical tools for testing theoreticalpredictions about the full behavior of the Hall conductivity for strongcorrelations.

Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model