2021/03/31 by Wen O. Wang, Jixun K. Ding, Brian Moritz +4 · 9 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Diagonal #Hamiltonian (control theory) #Hubbard model #Magnetic field #Mathematical physics #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum mechanics #Statistics #Superconductivity #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevresearch.3.033033
published in Physical Review Research 3(3) (American Physical Society) · 13 pages, 7 figures
openalex publication_date 2021/07/09 · arxiv created 2021/07/10 · arxiv updated 2021/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \ensuremathχxy in a system coupled to a finite magnetic field (FF), \ensuremathχxyFF; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, \ensuremathχxyZF; and the leading order of the recurrent expansion RH(0) in terms of thermodynamic susceptibilities. The two quantities \ensuremathχxyFF and \ensuremathχxyZF can be compared directly in imaginary time. Proxies for RH constructed from the three-current correlator \ensuremathχxyZF 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.