We obtain a set of general formulas for determining magnetizations, including the usual electromagnetic magnetization as well as the gravitomagnetic energy magnetization. The magnetization corrections to the thermal transport coefficients are explicitly demonstrated. Our theory provides a systematic approach for properly evaluating the thermal transport coefficients of magnetic systems, eliminating the unphysical divergence from the direct application of the Kubo formula. For a noninteracting anomalous Hall system, the corrected thermal Hall conductivity obeys the Wiedemann-Franz law.

We show that an effective magnetic field acting on phonons naturally emerges in the phonon dynamics of magnetic solids, giving rise to the phonon Hall effect. A general formula for the intrinsic phonon Hall conductivity is derived by using the corrected Kubo formula with the energy magnetization contribution incorporated properly. We thus establish a direct connection between the phonon Hall effect and the intrinsic phonon band structure, i.e., the phonon Berry curvature and phonon dispersion. Based on the formalism, we predict that phonons could also display the quantum Hall effect in certain topological phonon systems. In the low-temperature regime, we predict that the phonon Hall conductivity is proportional to T 3 for ordinary phonon systems, while that for the topological phonon system has a linear T dependence with a quantized temperature coefficient.

We review recent experimental and theoretical progress in realizing and simulating many-body phases of ultracold atoms in optical lattices, which gives access to analog quantum simulations of fundamental model Hamiltonians for strongly correlated condensed matter systems, such as the Hubbard model. After a general introduction to quantum gases in optical lattices, their preparation and cooling, and measurement techniques for relevant observables, we focus on several examples, where quantum simulations of this type have been performed successfully during the past years: Mott-insulator states, itinerant quantum magnetism, disorder-induced localization and its interplay with interactions, and topological quantum states in synthetic gauge fields.

Several examples of metallic electron doped polycyclic aromatic hydrocarbons (PAHs) molecular crystals have recently been experimentally proposed. Some of them have superconducting components, but most other details are still unknown beginning with structure and the nature of metallicity. We carried out ab-initio density functional calculations for La-Phenanthrene (La-PA), here meant to represent a generic case of three-electron doping, to investigate structure and properties of a conceptually simple case. To our surprise we found first of all that the lowest energy state is not metallic but band insulating, with a disproportionation of two inequivalent PA molecular ions and a low P 1 symmetry, questioning the common assumption that three electrons will automatically metallize a PAH crystal. Our best metallic structure is metastable and slightly higher in energy, and retains equivalent PA ions and a higher P 21 symmetry -the same generally claimed for metallic PAHs. We show that a "dimerizing" periodic distortion opens very effectively a gap in place of a symmetry related degeneracy of all P 21 structures near the Fermi level, foreshadowing a possible role of that special intermolecular phonon in superconductivity of metallic PAHs. A Hubbard-Fröhlich model describing that situation is formulated for future studies.

arXiv:1810.07710v2 [cond-mat.mes-hall]