Electrical conductivity in the Hubbard model: orbital effects of magnetic field
arXiv:2104.14578 · doi:10.1103/PhysRevB.104.205101
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 moiré systems.
32 pages, 21 figures
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- Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat
- Charge fluctuations, hydrodynamics and transport in the square-lattice Hubbard model
- Universal magnetic oscillations of DC conductivity in the incoherent regime of correlated systems
- Quantum oscillations in a doped Mott insulator beyond Onsager's relation
- Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator
- Low-frequency magnetic oscillations induced by strongly electron correlations
- Improved estimator for numerical renormalization group calculations of the self-energy