Quantum-Chemical Investigation of the Metal-Insulator Transition in realistic Low-Dimensional Systems
Zusammenfassung der Projektergebnisse
The clear distinction between metals and insulators is a well established and appartently simple concept which can be claried by studying the behavior of the electrical conductivity. However, a theoretical description of the processes leading to one of the two extremes is no trivial task. The widely accepted band structure theory relies on an one-electron picture to characterize the metallic/insulating behavior of a material. However, in spite of the fact that it can be used to make successful predictions, this description does not capture one of the essential elements characterizing the nature of an electronic quantum system, i.e. the electron correlation. The key to the different behaviors is clearly contained in the correlated many-electron wave function, but the analysis of such a high-dimensional object in conguration space can be quite cumbersome. Therefore the development of powerful tools to simplify this task is necessary. The total position-spread (TPS) tensor, which was derived by Walter Kohn's theory of the insulating state, plays a key role in the field of metal-insulator transitions (MITs). This tool provides information about the electron localization, which is strongly connected to the electrical conductivity. Therefore, in this work particular attention was paid to the calculation of the TPS tensor of small and extended systems. Moreover, part of this project focuses on a new formalism, which allows the study of spin mobility and spin entanglement and provides therefore deeper insight into the effects of electron correlation. In the framework of quantum information theory (QIT), the quantum entanglement can be quantied by means of measures such as the von Neumann entropy. Also, the analysis of the elements of the two-orbital reduced density matrix provides an overview of the complexity of the many-electron wave function. These insights were used in this work for the analysis of the metallic/insulating character of a system. However, in order to perform such investigastions, the problem of achieving an accurate description of the many-electron wave function has to be dealt with. Despite the tremedous progress in the effciency of quantum-chemical methods, the treatement of extended systems using standard approaches is still a difficult (if not unfeasible) task. Therefore the development and testing of sophisticated, low-scaling methods is currently the subject of many investigations. In this work, two approaches were employed: 1) the ab-initio density matrix renormalization group (DMRG) approach which, based on a tensor product ansatz, provides very precise results and exploits QIT to improve its performance; 2) the method of increments (MoI) which, using a many-body expansion in terms of localized orbitals, yields accurate correlation energies. By using both methods on strongly correlated one-dimesional model systems, we worked on a new formalism of the method of increments which can be used to describe the whole dissociation curve without inconvenient discontinuities. Finally, aiming to calculate the total position-spread tensor of extended systems, we worked on the application of the MoI for quantities other than the correlation energy.
Projektbezogene Publikationen (Auswahl)
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Ab-initio investigation of metal-insulator transitions in strongly correlated low-dimensional systems
E. Fertitta
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Investigation of metal-insulator-like transition through the ab-initio density matrix renormalization group approach. Phys. Rev. B90, 245129 (2014)
E. Fertitta, B. Paulus, G. Barcza, Ö. Legeza
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On the calculation of complete dissociation curves of closed-shell pseudo-one-dimensional systems via the complete active space method of increments. J. Chem. Phys.143, 114108 (2015)
E. Fertitta, B. Paulus, G. Barcza, Ö. Legeza
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Spin delocalization in hydrogen chains described with the spin-partitioned total position-spread tensor. Theor. Chem. Acc.134, 29 (2015)
M. El Khatib, O. Brea, E. Fertitta, G. L. Bendazzoli, S. Evangelisti, T. Leininger, B. Paulus
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The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains. J. Chem. Phys.143, 244308 (2015)
E. Fertitta, M. El Khatib, G. L. Bendazzoli, S. Evangelisti, T. Leininger, B. Paulus
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The total position-spread tensor: spin partition. J. Chem. Phys.142, 094113 (2015)
M. El Khatib, O. Brea, E. Fertitta, G. L. Bendazzoli, S. Evangelisti, T. Leininger
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Calculation of the static and dynamical correlation energy of pseudo-one-dimensional beryllium systems via a many-body expansion. J. Chem. Phys.145, 024104 (2016)
D. Koch, E. Fertitta, B. Paulus
