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Register a new userAnalytic continuation-free Greens function approach to correlated electronic structure calculations
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We present a new charge self-consistent scheme combining Density Functional and Dynamical Mean Field Theory, which uses Greens function of multiple scattering-type. In this implementation the many-body effects are incorporated into the Kohn-Sham iterative scheme without the need for the numerically ill-posed analytic continuation of the Greens function and of the self-energy. This is achieved by producing the Kohn-Sham Hamiltonian in the sub-space of correlated partial waves and allows to formulate the Greens function directly on the Matsubara axis. The spectral moments of the Matsubara Greens function enable us to put together the real space charge density, therefore the charge self-consistency can be achieved. Our results for the spectral functions (density of states) and equation of state curves for transition metal elements, Fe, Ni and FeAl compound agree very well with those of Hamiltonian based LDA+DMFT implementations. The current implementation improves on numerical accuracy, requires a minimal effort besides the multiple scattering formulation and can be generalized in several ways that are interesting for applications to real materials.
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We present SpM, a sparse modeling tool for the analytic continuation of imaginary-time Greens function, licensed under GNU General Public License version 3. In quantum Monte Carlo simulation, dynamic physical quantities such as single-particle and magnetic excitation spectra can be obtained by applying analytic continuation to imaginary-time data. However, analytic continuation is an ill-conditioned inverse problem and thus sensitive to noise and statistical errors. SpM provides stable analytic continuation against noise by means of a modern regularization technique, which automatically selects bases that contain relevant information unaffected by noise. This paper details the use of this program and shows some applications.
Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Greens function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the spectral function is inferred from a suitable set of parametrized basis functions. Bayesian model comparison then allows to assess the reliability of different parametrizations. The required evidence integrals of such a model comparison are determined by nested sampling. Compared to the maximum entropy method (MEM), routinely used for the analytic continuation of CTQMC data, the presented approach allows to infer whether the data support specific structures of the spectral function. We demonstrate the capability of BPAC in terms of CTQMC data for an Anderson impurity model (AIM) that shows a generalized Kondo scenario and compare the BPAC reconstruction to the MEM as well as to the spectral function obtained from the real-time fork tensor product state impurity solver where no analytic continuation is required. Furthermore, we present a combination of MEM and BPAC and its application to an AIM arising from the ab initio treatment of SrVO$_3$.
We revise critically existing approaches to evaluation of thermodynamic potentials within the Greens function calculations at finite electronic temperatures. We focus on the entropy and show that usual technical problems related to the multivalued nature of the complex logarithm can be overcome. This results in a simple expression for the electronic entropy, which does not require any contour integration in the complex energy plane. Properties of the developed formalism are discussed and its illustrating applications to selected model systems and to bcc iron with disordered local magnetic moments are presented as well.
We discuss a general approach to a realistic theory of the electronic structure in materials containing correlated d- or f- electrons. The main feature of this approach is the taking into account the energy dependence of the electron self-energy with the momentum dependence being neglected (local approximation). In the case of strong interactions (U/W>>1 - rare-earth system) the Hubbard-I approach is the most suitable. Starting from an exact atomic Green function with the constrained density matrix the band structure problem is formulated as the functional problem on Nmm for f-electrons and the standard LDA-functional for delocalized electrons. In the case of moderate correlations (U/W=1 metal-insulator regime) we start from the dynamical mean field iterative perturbation scheme (IPS) of G. Kotliar et. al. and also make use of our multiband atomic Green function. Finally for the weak interactions (U/W<1 -transition metals) the self-consistent diagrammatic fluctuation- exchange (FLEX)-approach of N. Bickers and D. Scalapino is generalized to the realistic multiband case. We presents two-band, two-dimensional model calculations for all three regimes. A realistic calculation in Hubbard-I scheme with the exact solution of the on-site multielectron problem for f(d)- shells was performed for mixed-valence 4f compound TmSe, and for the classical Mott insulator NiO.
The properties of symmetric nuclear and pure neutron matter are investigated within an extended self-consistent Greens function method that includes the effects of three-body forces. We use the ladder approximation for the study of infinite nuclear matter and incorporate the three-body interaction by means of a density-dependent two-body force. This force is obtained via a correlated average over the third particle, with an in-medium propagator consistent with the many-body calculation we perform. We analyze different prescriptions in the construction of the average and conclude that correlations provide small modifications at the level of the density-dependent force. Microscopic as well as bulk properties are studied, focusing on the changes introduced by the density dependent two-body force. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sum rule. Our results validate previously used uncorrelated averages and extend the availability of chirally motivated forces to a larger density regime.
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