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

Abstract

Using determinant quantum Monte Carlo, we compare three methods of evaluating the dc Hall coefficient of the Hubbard model: the direct measurement of the off-diagonal current-current correlator in a system coupled to a finite magnetic field (FF), ; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, ; and the leading order of the recurrent expansion in terms of thermodynamic susceptibilities. The two quantities and can be compared directly in imaginary time. Proxies for constructed from the three-current correlator can be determined under different simplifying assumptions and compared with . 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 , 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.