Reduced Density Matrix Based Models For Strongly Correlated Electrons
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Author | : Mohammad Mostafanejad |
Publisher | : |
Total Pages | : 0 |
Release | : 2020 |
Genre | : Chemistry, Physical and theoretical |
ISBN | : |
This dissertation presents a survey of ab initio models developed based on the merger of multireference (MR) methods and density functional theory (DFT) in order to provide an accurate and efficient description of electron correlation effects in strongly correlated systems. We first introduce a reduced density matrix (RDM)-based formulation of multiconfiguration pair-density functional theory (MC-PDFT) which addresses two of the three common problems in MR+DFT framework: double counting of the electron correlation and symmetry dilemma. MC-PDFT minimizes the double counting of electron correlation by computing the classical effects within MR part while accounting for quantum mechanical interactions via DFT part. Symmetry dilemma is also addressed through a change of variables from spin densities to on-top pair-density (OTPD). In order to resolve the third issue in MR+DFT framework, the computational cost barrier of the MR methods, we adopt the variational two-electron reduced density matrix (v2RDM)-driven complete active-space self-consistent field (CASSCF) approach. The favorable polynomial computational cost of v2RDM-CASSCF allows one to go beyond the active space size limitations of conventional configuration interaction (CI)-based MR methods. In order to reduce the delocalization error (DE) plaguing almost all density functionals, we extend MC-PDFT to its global and range-separated hybrid variants where a fraction of local exchange from OTPD functionals is replaced with its nonlocal counterpart computed by v2RDM-CASSCF reference RDMs. The efficiency and accuracy of our MC-PDFT-based models have also been demonstrated through their application to a wide variety of realistic and challenging molecular systems with dominant MR character such as the calculation of dissociation potential energy curves for di- and polyatomic molecules, reaction energy barriers of 1,3-dipolar cycloaddition reaction of ozone to ethylene and acetylene and singlet/triplet energy gaps of large members of oligocene molecular series. After providing numerical evidence for usefulness of our models for strongly correlated systems, we focus on the sources of errors and metrics for error quantification in DFT. Through introducing constrained search-Kohn-Sham density functional theory (CS-KSDFT), we have addressed two fundamental and controversial problems in KS-DFT: inaccessibility of the exact density within finite basis set and lack of a universal mathematical metric for the density error. Applying CS-KSDFT to strongly correlated systems, such as the triple-bond dissociation of N2, we have numerically showed that non-interacting KS-DFT electron densities can be far more accurate than those calculated by the conventional exchange-correlation (XC) functionals, regardless of the size of the basis set. By applying our basis set-independent metric to rank the performance of conventional density functionals for strongly correlated systems, we have numerically presented that the errors caused by the approximate forms of XC functionals (as opposed to density-driven errors) are the main source of error in KS-DFT. Lastly, we have analyzed the contentious onset of open-shell character in the singlet ground state zig-zag narrow graphene nanoribbons via a variety of metrics such as effectively unpaired electrons, natural orbital occupation numbers, singlet/triplet energy gaps and structural indicator of C-C bond length alternation.
Author | : David Sénéchal |
Publisher | : Springer Science & Business Media |
Total Pages | : 370 |
Release | : 2006-05-09 |
Genre | : Science |
ISBN | : 0387217177 |
Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type - i.e., problems where both localized and delocalized elements are present in low dimensions. The chapters are arranged in three parts. The first part deals with two of the most widely used numerical methods in strongly correlated electrons, the density matrix renormalization group and the quantum Monte Carlo method. The second part covers Lagrangian, Functional Integral, Renormalization Group, Conformal, and Bosonization methods that can be applied to one-dimensional or weakly coupled chains. The third part considers functional derivatives, mean-field, self-consistent methods, slave-bosons, and extensions.
Author | : Ghassan George Batrouni |
Publisher | : Springer Science & Business Media |
Total Pages | : 340 |
Release | : 2006-02-23 |
Genre | : Science |
ISBN | : 9780735403093 |
These proceedings cover the most recent developments in the fields of high temperature superconductivity, magnetic materials and cold atoms in traps. Special emphasis is given to recently developed numerical and analytical methods, such as effective model Hamiltonians, density matrix renormalization group as well as quantum Monte Carlo simulations. Several of the contributions are written by the pioneers of these methods.
Author | : Niravkumar D. Patel |
Publisher | : |
Total Pages | : 156 |
Release | : 2018 |
Genre | : Density matrices |
ISBN | : |
The interplay of magnetism and superconductivity in the iron-based superconductors is investigated numerically using Monte Carlo mean field and density matrix renormalization group methods. The finite temperature magnetic and transport properties of the 2D oxypnitides are calculated using Monte Carlo mean field methods, capturing many experimentally relevant phases and predicting a new phase dubbed "orbital selective directional conductor". Finally, pairing tendencies are explored using exact diagonalization and density matrix renormalization group for low dimensional iron-based superconductor, BaFe2S3, predicting hole pairs arranged along the diagonals or rungs of the ladders in real space. This dissertation further adds to the evidence that superconductivity in the iron based compounds has its origin in the magnetic fluctuations that are driven by correlations.
Author | : David Sénéchal |
Publisher | : Springer |
Total Pages | : 361 |
Release | : 2013-10-03 |
Genre | : Science |
ISBN | : 9781475780598 |
Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type - i.e., problems where both localized and delocalized elements are present in low dimensions. The chapters are arranged in three parts. The first part deals with two of the most widely used numerical methods in strongly correlated electrons, the density matrix renormalization group and the quantum Monte Carlo method. The second part covers Lagrangian, Functional Integral, Renormalization Group, Conformal, and Bosonization methods that can be applied to one-dimensional or weakly coupled chains. The third part considers functional derivatives, mean-field, self-consistent methods, slave-bosons, and extensions.
Author | : Vladimir E. Korepin |
Publisher | : World Scientific |
Total Pages | : 506 |
Release | : 1994 |
Genre | : Technology & Engineering |
ISBN | : 9789810215347 |
Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-c superconductivity and the fractional quantum hall effect. Analytical solutions to such models, though mainly limited to one spatial dimension, provide a complete and unambiguous picture of the dynamics involved. This volume is devoted to such solutions obtained using the Bethe Ansatz, and concentrates on the most important of such models, the Hubbard model. The reprints are complemented by reviews at the start of each chapter and an extensive bibliography.
Author | : Adolfo Avella |
Publisher | : Springer Science & Business Media |
Total Pages | : 350 |
Release | : 2013-04-05 |
Genre | : Science |
ISBN | : 3642351069 |
This volume presents, for the very first time, an exhaustive collection of those modern numerical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and material science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciate consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.
Author | : |
Publisher | : |
Total Pages | : 32 |
Release | : 1801 |
Genre | : |
ISBN | : |
Author | : David A. Mazziotti |
Publisher | : John Wiley & Sons |
Total Pages | : 300 |
Release | : 2007-04-06 |
Genre | : Science |
ISBN | : 047010659X |
An up-to-date account of this cutting-edge research in a consistent and understandable framework, of special interest to experts in other areas of electronic structure and/or quantum many-body theory. It will serve equally well as a self-contained guide to learning about reduced density matrices either through self-study or in a classroom as well as an invaluable resource for understanding the critical advancements in the field.
Author | : Stefan Rommer |
Publisher | : |
Total Pages | : 68 |
Release | : 1998 |
Genre | : |
ISBN | : 9789171976543 |