Common density-matrix functionals, the Müller and the power functional, have been benchmarked for the half-filled Hubbard dimer, which allows to model the bond dissociation problem and the transition from the weakly to the strongly correlated limit. Unbiased numerical calculations are combined with analytical results. Despite the well known successes of the Müller functional, the ground state is degenerate with a one-dimensional manifold of ferromagnetic solutions. The resulting infinite magnetic susceptibility indicates another qualitative flaw of the Müller functional. The derivative discontinuity with respect to particle number is not present indicating an incorrect metallike behavior. The power functional actually favors the ferromagnetic state for weak interaction. Analogous to the Hartree-Fock approximation, the power functional undergoes a transition beyond a critical interaction strength, in this case however, to a non-collinear antiferromagnetic state.

Abstract. In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or abinitio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green's functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.

Using ab initio calculations we reveal the nature of the insulating phase recently found experimentally in monolayer 1T-NbSe. We find soft phonon modes in a large part of the Brillouin zone indicating the strong-coupling nature of a charge-density-wave instability. Structural relaxation of a [Formula: see text] supercell reveals a Star-of-David reconstruction with an energy gain of 60 meV per primitive unit cell. The band structure of the distorted phase exhibits a half-filled flat band which is associated with orbitals that are delocalized over several atoms in each Star of David. By including many-body corrections through a combined GW, hybrid-functional, and DMFT treatment, we find the flat band to split into narrow Hubbard bands. The lowest energy excitation across the gap turns out to be between itinerant Se-p states and the upper Hubbard band, determining the system to be a charge-transfer insulator. Combined hybrid-functional and GW calculations show that long-range interactions shift the Se-p states to lower energies. Thus, a delicate interplay of local and long-range correlations determines the gap nature and its size in this distorted phase of the monolayer 1T-NbSe.

The qubit (or a system of two quantum dots) has become a standard paradigm for studying quantum information processes. Our focus is Decoherence due to interaction of the qubit with its environment, leading to noise. We consider quantum noise generated by a dissipative quantum bath. A detailed comparative study with the results for a classical noise source such as generated by a telegraph process, enables us to set limits on the applicability of this process vis a vis its quantum counterpart, as well as lend handle on the parameters that can be tuned for analyzing decoherence. Both Ohmic and non-Ohmic dissipations are treated and appropriate limits are analyzed for facilitating comparison with the telegraph process.