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Register a new userPerturbative calculation of non-local corrections to dynamical mean field theory
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A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron correlation the one-electron Greens function is strongly spatially damped so that its intersite matrix elements may be considered as small perturbations. Because the non-local corrections are at least quadratic in these matrix elements, DMFT in such cases may be a very accurate approximation in dimensions d = 1-3. This observation provides a rigorous justification for the application of DMFT to physical systems. Furthermore, the technique allows for a systematic evaluation of the nonlocal corrections. This is illustrated with the calculation of the magnetic short range order parameter for nearest neighbor spins in the half filled Hubbard model on the square lattice in its insulating phase which exhibits an excellent agreement with the results of a recent cluster approach.As a second example we study the lowest order correction to the DMFT self-energy and its influence on the local density of states.
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The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
To explore correlated electrons in the presence of local and non-local disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-frequency axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the non-interacting Bethe lattice with coordination number $Z$. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard $U$ parameter is increased, transitions from an alloy band-insulator through a correlated metal into a Mott insulating phase are found to take place.
Dynamical mean field methods are used to calculate the phase diagram, many-body density of states, relative orbital occupancy and Fermi surface shape for a realistic model of $LaNiO_3$-based superlattices. The model is derived from density functional band calculations and includes oxygen orbitals. The combination of the on-site Hunds interaction and charge-transfer between the transition metal and the oxygen orbitals is found to reduce the orbital polarization far below the levels predicted either by band structure calculations or by many-body analyses of Hubbard-type models which do not explicitly include the oxygen orbitals. The findings indicate that heterostructuring is unlikely to produce one band model physics and demonstrate the fundamental inadequacy of modeling the physics of late transition metal oxides with Hubbard-like models.
Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT). On top of this, non-local correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. We provide an overview of the successes and results achieved---hitherto mainly for model Hamiltonians---and outline future prospects for realistic material calculations.
Transition metal oxide heterostructures often, but by far not always, exhibit strong electronic correlations. State-of-the-art calculations account for these by dynamical mean field theory (DMFT). We discuss the physical situations in which DMFT is needed, not needed, and where it is actually not sufficient. By means of an example, SrVO$_3$/SrTiO$_3$, we discuss step-by-step and figure-by-figure a density functional theory(DFT)+DMFT calculation. The second part reviews DFT+DMFT calculations for oxide heterostructure focusing on titanates, nickelates, vanadates, and ruthenates.
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