Superconducting State in the Lagrangian Formalism of the Generalized Hubbard Model

The nonperturbative large-N expansion applied to the generalized Hubbard model describing N-fold-degenerate correlated bands is considered. Our previous results, obtained in the framework of the Lagrangian formalism for the normal-state case, are extended to the superconducting state. The standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. Our purpose is to obtain the 1/N corrections to the renormalized boson and fermion propagators when a state with Cooper-pair condensation (i.e., the superconducting state) is considered.     

Mott-Hubbard transition in a magnetic field

We study the density of states (DOS) as a function of the interaction U in the half-filled simplified Hubbard model in a magnetic field. This model is considered on the Bethe lattice in the limit of high dimensions. We show that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form. In particular, the DOS can be investigated explicitly in the limits of weak and strong coupling and near the metal-insulator transition. E.g., we find an explicit result for the critical value U_c, at which the metal-insulator transition occurs, as a function of the magnetization. The relation between the magnetization and the magnetic field is calculated numerically. An important result is that the metal-insulator transition, occurring in the model with B = 0, is continuously connected to the metal-insulator transition in the subspace of single spin flips.     

The nearest-neighbor resonating-valence bond state in a Grassmannian form

The nearest-neighbor resonating-valence bond (NNRVB) state is studied using classical anticommuting (Grassmann) variables. The classical partition function corresponding to the self-overlap of the NNRVB wavefunction is generated from a local (bond) Hamiltonian expressed in terms of four anticommuting variables. It is shown that the one-particle-per-site constraint introduces an interaction term which is a local product of all four variables. Two approaches are applied to study this Hamiltonian: (i) a self-consistent field decoupling scheme and (ii) a systematic perturbation expansion around the unconstrained soluble point. Bounds on the norm of the wavefunction are derived. Extensions to the presence of holes, long-range valence bonds, and the introduction of phase fluctuations [which violate the Marshall sign rule and yield aU(1) gauge theory] are discussed.     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

The Different Story of π Bonds

We revisit “classical” issues in multiply bonded systems between main groups elements, namely the structural distortions that may occur at the multiple bonds and that lead, e.g., to trans-bent and bond-length alternated structures. The focus is on the role that orbital hybridization and electron correlation play in this context, here analyzed with the help of simple models for σ- and π-bonds, numerically exact solutions of Hubbard Hamiltonians and first principles (density functional theory) investigations of an extended set of systems.     

Nonequilibrium Green Functions Approach to Strongly Correlated Fermions in Lattice Systems

Quantum dynamics in strongly correlated systems are of high current interest in many fields including dense plasmas, nuclear matter and condensed matter and ultracold atoms. An important model case are fermions in lattice systems that is well suited to analyze, in detail, a variety of electronic and magnetic properties of strongly correlated solids. Such systems have recently been reproduced with fermionic atoms in optical lattices which allow for a very accurate experimental analysis of the dynamics and of transport processes such as diffusion. The theoretical analysis of such systems far from equilibrium is very challenging since quantum and spin effects as well as correlations have to be treated non‐perturbatively. The only accurate method that has been successful so far are density matrix renormalization group (DMRG) simulations. However, these simulations are presently limited to one‐dimensional (1D) systems and short times. Extension of quantum dynamics simulations to two and three dimensions is commonly viewed as one of the major challenges in this field. Recently we have reported a breakthrough in this area [N. Schlünzen et al., Phys. Rev. B (2016)] where we were able to simulate the expansion dynamics of strongly correlated fermions in a Hubbard lattice following a quench of the confinement potential in 1D, 2D and 3D. The results not only exhibited excellent agreement with the experimental data but, in addition, revealed new features of the short‐time dynamics where correlations and entanglement are being build up. The method used in this work are nonequilibrium Green functions (NEGF) which are found to be very powerful in the treatment of fermionic lattice systems filling the gap presently left open by DMRG in 2D and 3D. In this paper we present a detailed introduction in the NEGF approach and its application to inhomogeneous Hubbard clusters. In detail we discuss the proper strong coupling approximation which is given by T ‐matrix selfenergies that sum up two‐particle scattering processes to infinite order. The efficient numerical implemen‐tation of the method is discussed in detail as it has allowed us to achieve dramatic performance gains. This has been the basis for the treatment of more than 100 particles over large time intervals. The numerical results presented in this paper concentrate on the diffusion in 1D to 3D lattices. We find that the expansion dynamics consist of three different phases that are linked with the build‐up of correlations. In the long time limit, a universal scaling with the particle number is revealed. By extrapolating the expansion velocities to the macroscopic limit, the obtained results show excellent agreement with recent experiments on ultracold fermions in optical lattices. Moreover we present results for the site‐resolved behavior of correlations and entanglement that can be directly compared with experiments using the recently developed atomic microscope technique. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ferromagnetism,spiral magnetic structures and phase separation in the two-dimensional Hubbard model

The quasistatic approximation and equation-of-motion decoupling for the electron Green's functions are applied to trace the effect of electronic dispersion and electron correlations on the ferromagnetism of two-dimensional itinerant-electron systems. It is found that next-nearest-neighbor hopping t′$t\prime$ is of crucial importance for ferromagnetism formation yielding the magnetic phase diagram which is strongly asymmetric with respect to half-filling. At small t′$t\prime$ in the vicinity of half-filling the ferromagnetic phase region is restricted by the spin-density wave instability, and far from half-filling by one-particle (spin-polaron) instability. At t′$t\prime$ close to t/2$t/2$ ferromagnetism is stabilized at moderate Hubbard U   due to substantial curvature of the Fermi surface which passes in the vicinity of the van Hove singularity points. The results obtained are of possible importance for high-_Tc$T_{\mathrm{c}}$ compounds and layered ruthenates.     

Variational local moment approach: From Kondo effect to Mott transition in correlated electron systems

The variational local moment approach (VLMA) solution of the single impurity Anderson model is presented. It generalizes the local moment approach of Logan et al. by invoking the variational principle to determine the lengths of local moments and orbital occupancies. We show that VLMA is a comprehensive, conserving and thermodynamically consistent approximation and treats both Fermi and non-Fermi liquid regimes as well as local moment phases on equal footing. We tested VLMA on selected problems. We solved the single- and multi-orbital impurity Anderson model in various regions of parameters, where different types of Kondo effects occur. The application of VLMA as an impurity solver of the dynamical mean-field theory, used to solve the multi-orbital Hubbard model, is also addressed.     

Constrained Density Functional Theory Plus the Hubbard U Correction Approach for the Electronic Polaron Mobility: A Case Study of TiO2?

The formation and migration of polarons have important influences on physical and chemical properties of transition metal oxides. Density functional theory plus the Hubbard \begin{document}$U$\end{document} correction (DFT+\begin{document}$U$\end{document}) and constrained density functional theory (cDFT) are often used to obtain the transfer properties for small polarons. In this work we have implemented the cDFT plus the Hubbard \begin{document}$U$\end{document} correction method in the projector augmented wave (PAW) framework, and applied it to study polaron transfer in the bulk phases of TiO\begin{document}$_2$\end{document}. We have confirmed that the parameter \begin{document}$U$\end{document} can have significant impact on theoretical prediction of polaronic properties. It was found that using the Hubbard \begin{document}$U$\end{document} calculated by the cDFT method with the same orbital projection as used in DFT+\begin{document}$U$\end{document}, one can obtain theoretical prediction of polaronic properties of rutile and anatase phases of TiO\begin{document}$_2$\end{document} in good agreement with experiment. This work indicates that the cDFT+\begin{document}$U$\end{document} method with consistently evaluated \begin{document}$U$\end{document} is a promising first-principles approach to polaronic properties of transition metal oxides without empirical input.