arXiv:1802.04810 · Physical Review Letters

Hall Number of Strongly Correlated Metals

Assa Auerbach

Published Aug 6, 2018• 34 citations

Abstract

An exact formula for the temperature dependent Hall number of metals is derived. It is valid for nonrelativistic fermions or bosons, with an arbitrary potential and interaction. This dc transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.

DOI: 10.1103/physrevlett.121.066601

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arXiv:1802.04810 · Physical Review Letters

Hall Number of Strongly Correlated Metals

Assa Auerbach

Published Aug 6, 2018• 34 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.121.066601

Related papers

DC Hall coefficient of the strongly correlated Hubbard model

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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.

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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 ${\ensuremath{\chi}}_{xy}$ 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

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.