DC Hall coefficient of the strongly correlated Hubbard model

Wen O Wang,Thomas P Devereaux,Edwin W Huang,Brian Moritz,Jixun K Ding

doi:10.1038/s41535-020-00254-w

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.

Highlights

The Hall coefficient RH reveals properties of band structure and effective carrier density in weakly interacting systems, determined by the shape of the Fermi surface and the angular dependence of the quasiparticle relaxation time[1,2]
Quantum Monte Carlo (QMC) simulations on the Hubbard model show similar generic nature of the quasiparticle dispersion relation observed in some hole-doped cuprates, and demonstrate it to be mostly determined by the strong Coulomb repulsion, reflecting many-body correlations, rather than a one-electron band structure[26]
Along with T-linear resistivity in the Hubbard model[25], both phenomena suggest that strongly correlated electrons shouldn’t behave like coherent quasiparticles moving in a static band structure

Summary

INTRODUCTION

The Hall coefficient RH reveals properties of band structure and effective carrier density in weakly interacting systems, determined by the shape of the Fermi surface and the angular dependence of the quasiparticle relaxation time[1,2]. Hubbard model calculations have revealed properties similar to those of high-Tc cuprates, including T-linear resistivity in the strange metal phase[25]. Quantum Monte Carlo (QMC) simulations on the Hubbard model show similar generic nature of the quasiparticle dispersion relation observed in some hole-doped cuprates, and demonstrate it to be mostly determined by the strong Coulomb repulsion, reflecting many-body correlations, rather than a one-electron band structure[26]. We find strong temperature and doping dependence of RH in a parameter regime with strong interactions and no coherent quasiparticles, and show a good correspondence between the sign of the Hall coefficient and the shape of a quasi-Fermi surface

RESULTS

DISCUSSION

METHODS

CODE AVAILABILITY