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

Wang, Wen O.; Ding, Jixun K.; Moritz, Brian; Schattner, Yoni; Huang, Edwin W.; Devereaux, Thomas P.

doi:10.1103/PhysRevResearch.3.033033

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

Journal Article · Fri Jul 09 00:00:00 EDT 2021 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.3.033033· OSTI ID:1806591

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

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231; AC02-76SF00515

OSTI ID:: 1806591

Alternate ID(s):: OSTI ID: 1797882

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Vol. 3 Journal Issue: 3; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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

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