Vanadium dioxide undergoes a first order metal-insulator transition at 340 K. In this Letter, we develop and carry out state-of-the-art linear scaling density-functional theory calculations refined with nonlocal dynamical mean-field theory. We identify a complex mechanism, a Peierls-assisted orbital selection Mott instability, which is responsible for the insulating $M_1$ phase, and which furthermore survives a moderate degree of disorder.

We use the local-density approximation in combination with the dynamical mean-field theory to carry out a comparative investigation of a typical electron-doped and a typical hole-doped copper oxide, NCCO, and LSCO, respectively. The parent compounds of both materials are strongly correlated electron systems in the vicinity of the metal to charge-transfer insulator transition. In NCCO the magnetic long-range order is essential to open a charge-transfer gap while Mott physics is responsible for the gap in LSCO. We highlight the role of the apical oxygens in determining the strength of the correlations and obtaining overall good agreement between theory and several experimentally determined quantities. Results for optical conductivity, polarized x-ray absorption, and angle-resolved photoemission are presented and compared with experiments.

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for $J_2/J_1>1/2$, thermal fluctuations give rise to an effective $Z_2$ symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that $T_c\to 0$ with an infinite slope when $J_2/J_1\to 1/2$.

Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters and that they are stabilized in the thermodynamic limit if additional interactions, e.g., strong hybridization with apical oxygens, are included in the model.