Electrical conductivity in the Hubbard model: orbital effects of magnetic field

TL;DR

This paper develops a formalism for calculating orbital magnetic field effects on conductivity in the Hubbard model, demonstrating gauge invariance, vertex correction cancellation in DMFT, and analyzing quantum oscillations consistent with experiments.

Contribution

It provides a detailed formalism for conductivity calculations in the Hubbard model under magnetic fields, including DMFT simplifications and analysis of quantum oscillations.

Findings

Vertex corrections cancel in DMFT regardless of magnetic field.

Spectral function and conductivity are computed across parameter regimes.

Quantum oscillations in conductivity match recent experimental observations.

Abstract

Calculation of conductivity in the Hubbard model is a challenging task. Recent years have seen much progress in this respect and numerically exact solutions are now possible in certain regimes. In this paper we discuss the calculation of conductivity for the square lattice Hubbard model in the presence of a perpendicular magnetic field, focusing on orbital effects. We present the relevant formalism in all detail and in full generality, and then discuss the simplifications that arise at the level of the dynamical mean field theory (DMFT). We prove that the Kubo bubble preserves gauge and translational invariance, and that in the DMFT the vertex corrections cancel regardless of the magnetic field. We present the DMFT results for the spectral function and both the longitudinal and Hall conductivity in several regimes of parameters. We analyze thoroughly the quantum oscillations of the longitudinal conductivity and identify a high-frequency oscillation component, arising as a combined effect of scattering and temperature, in line with recent experimental observations in moir\'e systems.