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

TL;DR

This paper compares three numerical methods using determinant Quantum Monte Carlo to evaluate the dc Hall coefficient in the doped Hubbard model, validating their consistency and the link between Fermi surface topology and Hall sign.

Contribution

It introduces and compares three computational approaches for calculating the dc Hall coefficient in the Hubbard model, confirming their agreement and usefulness for studying strong correlations.

Findings

Different methods yield consistent results for $R_H$

Validated the link between Fermi surface topology and Hall sign

Provided numerical tools for analyzing Hall conductivity in correlated systems

Abstract

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 $\chi_{xy}$ in a system coupled to a finite magnetic field (FF), $\chi_{xy}^{\text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, $\chi_{xy}^{\text{ZF}}$; and the leading order of the recurrent expansion $R_H^{(0)}$ in terms of thermodynamic susceptibilities. The two quantities $\chi_{xy}^{\text{FF}}$ and $\chi_{xy}^{\text{ZF}}$ can be compared directly in imaginary time. Proxies for $R_H$ constructed from the three-current correlator $\chi_{xy}^{\text{ZF}}$ can be determined under different simplifying assumptions and compared with $R_H^{(0)}$. 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.