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Register a new userConservation in two-particle self-consistent extensions of dynamical-mean-field-theory
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Added by
Alexander Lichtenstein
Publication date
2017
fields
Physics
and research's language is
English
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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.
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We propose a hybrid approach which employs the dynamical mean-field theory (DMFT) self-energy for the correlated, typically rather localized orbitals and a conventional density functional theory (DFT) exchange-correlation potential for the less correlated, less localized orbitals. We implement this self-energy (plus charge density) self-consistent DFT+DMFT scheme in a basis of maximally localized Wannier orbitals using Wien2K, wien2wannier, and the DMFT impurity solver w2dynamics. As a testbed material we apply the method to SrVO$_3$ and report a significant improvement as compared to previous $d$+$p$ calculations. In particular the position of the oxygen $p$ bands is reproduced correctly, which has been a persistent hassle with unwelcome consequences for the $d$-$p$ hybridization and correlation strength. Taking the (linearized) DMFT self-energy also in the Kohn-Sham equation renders the so-called double-counting problem obsolete.
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.
We employ the jackknife algorithm to analyze the propagation of the statistical quantum Monte Carlo error through the Bethe--Salpeter equation. This allows us to estimate the error of dynamical mean-field theory calculations of the susceptibility and of dynamical vertex approximation calculations of the self-energy. We find that the different frequency components of the susceptibility are uncorrelated, whereas those of the self-energy are correlated. For improving the quality of the correlation matrix taking sufficiently many jackknife bins is key, while for reducing the standard error of the mean sufficiently many Monte Carlo measurements are necessary. We furthermore show that even in the case of the self-energy, the finite covariance does not have a sizable influence on the analytic continuation.
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.
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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