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 $R_H$ 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.

arXiv comment13 pages, 7 figures

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Cited by in corpus (7)

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• Magnon heat transport in a two-dimensional Mott insulator
• Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator
• Quantum Transport Theory of Strongly Correlated Matter
• Effects of the pseudogap and the Fermi surface on the rapid Hall-coefficient changes in cuprates
• Intrinsic Thermal Hall Effect in Mott Insulators
• Construction of the spectral function from non-commuting spectral moment matrices