Using determinant quantum Monte Carlo, we compare three methods of evaluating the dc Hall coefficient $R_H$ of the Hubbard model: the direct measurement of the off-diagonal current-current correlator ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{xy}$ in a system coupled to a finite magnetic field (FF), ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{xy}^{\text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{xy}^{\text{ZF}}$; and the leading order of the recurrent expansion $R_H^{\left(0\right)}$ in terms of thermodynamic susceptibilities. The two quantities ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{xy}^{\text{FF}}$ and ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{xy}^{\text{ZF}}$ can be compared directly in imaginary time. Proxies for $R_H$ constructed from the three-current correlator ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{xy}^{\text{ZF}}$ can be determined under different simplifying assumptions and compared with $R_H^{\left(0\right)}$. We find these different quantities to be consistent with one another, validating previous conclusions about the close correspondence between Fermi surface topology and the sign of $R_H$, even for strongly correlated systems. These various quantities also provide a useful set of numerical tools for testing theoretical predictions about the full behavior of the Hall conductivity for strong correlations.

• Received 8 March 2021
• Revised 9 June 2021
• Accepted 10 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033033

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society