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Register a new userEfficient treatment of two-particle vertices in dynamical mean-field theory
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Authors
Jan Kunes
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We present an efficient and numerically stable algorithm for calculation of two-particle response functions within the dynamical mean-field theory. The technique is based on inferring the high frequency asymptotic behavior of the irreducible vertex function from the local dynamical susceptibility. The algorithm is tested on several examples. In all cases rapid convergence of the vertex function towards its asymptotic form is observed.
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We present here two alternative schemes designed to correct the high-frequency truncation errors in the numerical treatment of the Bethe-Salpeter equations. The schemes are applicable to all Bethe-Salpeter calculations with a local two-particle irreducible local, which is relevant, e.g., for the dynamical mean-field theory (DMFT) and its diagrammatic extensions. In particular, within a purely diagrammatic framework, we could extend existing algorithms for treating the static case in the particle-hole sector to more general procedures applicable to all bosonic frequencies and all channels. After illustrating the derivation and the theoretical interrelation of the two proposed schemes, these have been applied to the Bethe-Salpeter equations for the auxiliary Anderson impurity models of selected DMFT calculations, where results can be compared against a numerically exact solution. The successful performance of the proposed schemes suggests that their implementation can significantly improve the accuracy of dynamical mean-field theory (DMFT) calculations at the two-particle level, in particular for more realistic multi-orbital calculations where the large number of degrees of freedom substantially restricts the actual frequency range for numerical calculations, as well as -on a broader perspective- of the diagrammatic extensions of DMFT.
Extensions of dynamical-mean-field-theory (DMFT) make use of quantum impurity models as non-perturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of retarded interactions on the impurity, these approximations can be made two-particle self-consistent. This is of interest for the Hubbard model, because it allows to suppress the antiferromagnetic phase transition in two-dimensions in accordance with the Mermin-Wagner theorem, and to include the effects of bosonic fluctuations. For a physically sound description of the latter, the approximation should be conserving. In this paper we show that the mutual requirements of two-particle self-consistency and conservation lead to fundamental problems. For an approximation that is two-particle self-consistent in the charge- and longitudinal spin channel, the double occupancy of the lattice and the impurity are no longer consistent when computed from single-particle properties. For the case of self-consistency in the charge- and longitudinal as well as transversal spin channels, these requirements are even mutually exclusive so that no conserving approximation can exist. We illustrate these findings for a two-particle self-consistent and conserving DMFT approximation.
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.
We present an efficient ab initio dynamical mean-field theory (DMFT) implementation for quantitative simulations in solids. Our DMFT scheme employs ab initio Hamiltonians defined for impurities comprising the full unit cell or a supercell of atoms and for realistic quantum chemical basis sets. We avoid double counting errors by using Hartree-Fock as the low-level theory. Intrinsic and projected atomic orbitals (IAO+PAO) are chosen as the local embedding basis, facilitating numerical bath truncation. Using an efficient integral transformation and coupled-cluster Greens function (CCGF) impurity solvers, we are able to handle embedded impurity problems with several hundred orbitals. We apply our ab initio DMFT approach to study a hexagonal boron nitride monolayer, crystalline silicon, and nickel oxide in the antiferromagnetic phase, with up to 104 and 78 impurity orbitals in spin-restricted and unrestricted cluster DMFT calculations and over 100 bath orbitals. We show that our scheme produces accurate spectral functions compared to both benchmark periodic coupled-cluster computations and experimental spectra.
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.
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