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 ${\ensuremath{\chi}}_{xy}$ in a system coupled to a finite magnetic field (FF), ${\ensuremath{\chi}}_{xy}^{\text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$; and the leading order of the recurrent expansion ${R}_{H}^{(0)}$ in terms of thermodynamic susceptibilities. The two quantities ${\ensuremath{\chi}}_{xy}^{\text{FF}}$ and ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$ can be compared directly in imaginary time. Proxies for ${R}_{H}$ constructed from the three-current correlator ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$ 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.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 ${\ensuremath{\chi}}_{xy}$ in a system coupled to a finite magnetic field (FF), ${\ensuremath{\chi}}_{xy}^{\text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$; and the leading order of the recurrent expansion ${R}_{H}^{(0)}$ in terms of thermodynamic susceptibilities. The two quantities ${\ensuremath{\chi}}_{xy}^{\text{FF}}$ and ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$ can be compared directly in imaginary time. Proxies for ${R}_{H}$ constructed from the three-current correlator ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$ 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:2103.04998Physical Review ResearchJul 9, 202110 citations

DC Hall coefficient of the strongly correlated Hubbard model

Wen O. Wang, Jixun K. Ding, Brian Moritz +2 more

Abstract The Hall coefficient is related to the effective carrier density and Fermi surface topology in non-interacting and weakly interacting systems. In strongly correlated systems, the relation between the Hall coefficient and single-particle properties is less clear. Clarifying this relation would give insight into the nature of transport in strongly correlated materials that lack well-formed quasiparticles. In this work, we investigate the DC Hall coefficient of the Hubbard model using determinant quantum Monte Carlo in conjunction with a recently developed expansion of magneto-transport coefficients in terms of thermodynamic susceptibilities. At leading order in the expansion, we observe a change of sign in the Hall coefficient as a function of temperature and interaction strength, which we relate to a change in the topology of the apparent Fermi surface. We also combine our Hall coefficient results with optical conductivity values to evaluate the Hall angle, as well as effective mobility and effective mass based on Drude theory of metals.Abstract The Hall coefficient is related to the effective carrier density and Fermi surface topology in non-interacting and weakly interacting systems. In strongly correlated systems, the relation between the Hall coefficient and single-particle properties is less clear. Clarifying this relation would give insight into the nature of transport in strongly correlated materials that lack well-formed quasiparticles. In this work, we investigate the DC Hall coefficient of the Hubbard model using determinant quantum Monte Carlo in conjunction with a recently developed expansion of magneto-transport coefficients in terms of thermodynamic susceptibilities. At leading order in the expansion, we observe a change of sign in the Hall coefficient as a function of temperature and interaction strength, which we relate to a change in the topology of the apparent Fermi surface. We also combine our Hall coefficient results with optical conductivity values to evaluate the Hall angle, as well as effective mobility and effective mass based on Drude theory of metals.

arXiv:2002.12289npj Quantum MaterialsJul 24, 202024 citations

Quantum Hall Physics in Low-Dimensional Strongly Correlated Systems

Kun Yang

Jan 1, 19940 citations

Memory function approach to the Hall constant in strongly correlated electron systems: Part II

Ekkehard Lange

The anomalous frequency and doping dependence of the Hall constant in the normal state of high-T_c superconductors are investigated within models of strongly correlated electron systems. In Mori theory, the transition of the Hall constant from infinite to zero frequency is described by a memory function. It naturally introduces a second time scale, that, within the t-J model, is identified with the spinon relaxation time of Anderson. This provides us with a phenomenological understanding of the interplay between the frequency and temperature dependence of the Hall constant for frequencies below the Mott-Hubbard gap. Within the single-band Hubbard model in the limit $U\gg t$ , the memory function is calculated via its moments and shown to project out the high-energy scale U. This causes the Hall constant to decrease by a factor $(1+δ)/2$ ( $δ$ : doping), when the frequency is lowered from infinity to values within the Mott-Hubbard gap. Finally, it is outlined, how the Hall constant may be calculated in the low frequency regime.The anomalous frequency and doping dependence of the Hall constant in the normal state of high-T_c superconductors are investigated within models of strongly correlated electron systems. In Mori theory, the transition of the Hall constant from infinite to zero frequency is described by a memory function. It naturally introduces a second time scale, that, within the t-J model, is identified with the spinon relaxation time of Anderson. This provides us with a phenomenological understanding of the interplay between the frequency and temperature dependence of the Hall constant for frequencies below the Mott-Hubbard gap. Within the single-band Hubbard model in the limit $U\gg t$, the memory function is calculated via its moments and shown to project out the high-energy scale U. This causes the Hall constant to decrease by a factor $(1+δ)/2$ ($δ$: doping), when the frequency is lowered from infinity to values within the Mott-Hubbard gap. Finally, it is outlined, how the Hall constant may be calculated in the low frequency regime.

arXiv:cond-mat/9611050Nov 7, 19960 citations

High correlation regime of the Hubbard model

Miguel Lagos, Miguel Kiwi, R. Ramirez

Solid State CommunicationsAug 1, 19880 citations

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 ${\ensuremath{\chi}}_{xy}$ in a system coupled to a finite magnetic field (FF), ${\ensuremath{\chi}}_{xy}^{\text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$; and the leading order of the recurrent expansion

{R}_{H}^{(0)}

in terms of thermodynamic susceptibilities. The two quantities ${\ensuremath{\chi}}_{xy}^{\text{FF}}$ and ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$ can be compared directly in imaginary time. Proxies for

{R}_{H}

constructed from the three-current correlator ${\ensuremath{\chi}}_{xy}^{\text{ZF}}$ 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.

U\gg t

, the memory function is calculated via its moments and shown to project out the high-energy scale U. This causes the Hall constant to decrease by a factor

(1+δ)/2

(

δ

: doping), when the frequency is lowered from infinity to values within the Mott-Hubbard gap. Finally, it is outlined, how the Hall constant may be calculated in the low frequency regime.