The double perovskite ${rm La}_2{rm NiTiO}_6$ is identified as a three-dimensional $S=1$ quantum magnet. By means of Density Functional Theory we demonstrate that this material is a high-spin $d$-electron system deep in the Heisenberg limit and estab
lish that its paramagnetic Mott phase persists down to low temperatures ($T_{rm N}$=25K) not because of frustration effects but rather for the extreme strong coupling physics. Our many-body calculations on an $ab$ $initio$-derived multi-orbital basis predict indeed a kinetic energy gain when entering the magnetically ordered phase. ${rm La}_2{rm NiTiO}_6$ emerges thus as a paradigmatic realization of a spin-triplet Mott insulator. Its peculiar properties may turn out to be instrumental in the ongoing chase after correlated topological states of matter.
In the context of realistic calculations for strongly-correlated materials with $d$- or $f$-electrons the efficient computation of multi-orbital models is of paramount importance. Here we introduce a set of invariants for the SU(2)-symmetric Kanamori
Hamiltonian which allows to massively speed up the calculation of the fermionic trace in hybridization-expansion continuous-time quantum Monte Carlo algorithms. As an application, we show that, exploiting this set of good quantum numbers, the study of the orbital-selective Mott-transition in systems with up to seven correlated orbitals becomes feasible.
By means of a Wannier projection within the framework of density functional theory, we are able to identify the modified c-axis hopping and the energy mismatch between the cation bands as the main source of the $t_{2g}$ splitting around the $Gamma$ p
oint for oxide heterostructures, excluding previously proposed mechanisms such as Jahn-Teller distortions or electric field asymmetries. Interfacing LaAlO$_3$, LaVO$_3$, SrVO$_3$ and SrNbO$_3$ with SrTiO$_3$ we show how to tune this orbital splitting, designing heterostructures with more $d_{xy}$ electrons at the interface. Such an orbital engineering is the key for controlling the physical properties at the interface of oxide heterostructures.
The effects of an electron-phonon ($e$-ph) interaction on the thermoelectric properties of Na$_x$CoO$_2$ are analyzed. By means of dynamical mean field theory calculations we find that the $e$-ph coupling acts in a cooperative way with the disorder,
enhancing the effective binary disorder potential strength on the Co sites, which stems from the presence or absence of a neighboring Na atom. Hence, the inclusion of the $e$-ph coupling allows us to assume smaller values of the binary disorder potential strength -- which for Na$_x$CoO$_2$ are in fact also more reasonable. More generally, we can conclude that the interplay between disorder effects and coupling to the lattice can be exploited to engineer more efficient thermoelectric materials.
We study cuprates within Dynamical Cluster Approximation and find the pseudogap displays an isotope effect of the same sign as observed experimentally. Notwithstanding the non-phononic origin of the pseudogap the interplay between electronic repulsio
n and retarded phonon-mediated attraction gives rise to an isotope dependence of the antinodal spectra. Due to the strong momentum differentiation, such interplay is highly non-trivial and leads to the simultaneous presence of heavier quasiparticles along the nodal direction. We predict an isotope effect in electron-doped materials.
We improve on Fourier transforms (FT) between imaginary time $tau$ and imaginary frequency $omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Greens function can be improved by us
ing a sumrule boundary condition for a spline. For response functions a two-dimensional FT of a singular function is required. We show how this can be done efficiently by splitting off a one-dimensional part containing the singularity and by performing a semi-analytical FT for the remaining more innocent two-dimensional part.
