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

Wen O. Wang1,*, Jixun K. Ding1, Brian Moritz2, Yoni Schattner2,3, Edwin W. Huang4, and Thomas P. Devereaux2,5,†

  • 1Department of Applied Physics, Stanford University, Stanford, California 94305, USA
  • 2Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
  • 3Department of Physics, Stanford University, Stanford, California 94305, USA
  • 4Department of Physics and Institute of Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 5Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA

  • *wenwang.physics@gmail.com
  • †tpd@stanford.edu
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Phys. Rev. Research 3, 033033 – Published 9 July, 2021

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

Abstract

Using determinant quantum Monte Carlo, we compare three methods of evaluating the dc Hall coefficient RH of the Hubbard model: the direct measurement of the off-diagonal current-current correlator χxy in a system coupled to a finite magnetic field (FF), χxyFF; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, χxyZF; and the leading order of the recurrent expansion RH(0) in terms of thermodynamic susceptibilities. The two quantities χxyFF and χxyZF can be compared directly in imaginary time. Proxies for RH constructed from the three-current correlator χxyZF can be determined under different simplifying assumptions and compared with RH(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 RH, 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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Phys. Rev. Research 3, 033033– Published 9 July, 2021
  • Received 8 March 2021
  • Revised 9 June 2021
  • Accepted 10 June 2021
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