Ferromagnetic Weyl semi-metals exhibit an anomalous Hall effect, a consequence of their topological properties. In the non-interacting case, the derivative of the orbital magnetization with respect to chemical potential is proportional to this anomalous Hall effect, the Středa formula. Motivated by compounds such as Mn3Sn, here we investigate how interactions modeled by a Hubbard U impact on both quantities when the Fermi energy is either aligned with the Weyl nodes or away from them. Using Dynamical Mean-Field Theory, we first find interaction-induced Mott-and band-insulating transitions. In the Weyl semimetal regime, away from insulators, interactions lead to an increase in the imbalance between the densities of spin species induced by a Zeeman term h. This increased imbalance leads to an increase of the anomalous Hall effect that can also be understood from the displacement of the Weyl nodes and topological arguments. This interaction-induced spin imbalance also compensates the reduction in orbital magnetization of each spin species that comes from smaller quasiparticle weight. In the small inteaction regime, the combined effects lead to an orbital magnetization that depends weakly on interaction and still changes linearly with chemical potential at small doping. In the intermediate and strong correlation regimes, the localization due to interaction affects strongly the orbital magnetization, which becomes small. A quasiparticle picture explains the anomalous Hall effect but does not suffice for the orbital magnetization. We propose a modified Středa formula to relate anomalous Hall effect and orbital magnetization in the weak correlation limit. We also identify mirror and particle-hole symmetries of the lattice model that explain, respectively, the vanishing of the anomalous Hall effect at h = 0 for all U and of the orbital magnetization at half-filling, µ = 0, for all U and h. arXiv:1807.07508v2 [cond-mat.str-el]

Spin-liquid behavior was recently suggested experimentally in the moderately one-dimensional organic compound κ-H3(Cat-EDT-TTF)2. This compound can be modeled by the one-band Hubbard model on the anisotropic triangular lattice with t /t 1.5, where t is the minority hopping. It thus becomes important to extend previous studies, that were performed in the range 0 ≤ t /t ≤ 1.2, to find out whether there is a regime where Mott insulating behavior can be found without longrange magnetic order. To this end, we study the above model in the range 1.2 ≤ t /t ≤ 2 using cluster dynamical mean-field theory (CDMFT). We argue that it is important to choose a symmetrypreserving cluster rather than a quasi one-dimensional cluster. We find that, upon increasing t /t beyond t /t ≈ 1.3, the Mott transition at zero-temperature is replaced by a first-order transition separating a metallic state from a collinear magnetic insulating state. Nevertheless, at the physically relevant value t /t 1.5, the transitions toward the magnetic and the Mott insulating phases are very close. The phase diagram obtained in this study can provide a working basis for moderately one-dimensional compounds on the anisotropic triangular lattice.

The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms, calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical meanfield theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the singleparticle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime. II. THE DYNAMICAL MEAN-FIELD EQUATIONS WITH MAGNETIC FIELDHere we derive 17 the DMFT equations when the orbital effect of the magnetic field is taken into account in arXiv:1710.01396v1 [cond-mat.str-el]