Cluster Dynamical Mean Field Theory Of Strongly Correlated Superconductivity Magnetism
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Dynamical Mean-Field Theory for Strongly Correlated Materials
Author | : Volodymyr Turkowski |
Publisher | : Springer Nature |
Total Pages | : 393 |
Release | : 2021-04-22 |
Genre | : Technology & Engineering |
ISBN | : 3030649040 |
This is the first book that provides a detailed summary of one of the most successful new condensed matter theories - dynamical mean-field theory (DMFT) - in both static and dynamical cases of systems of different sizes. DMFT is one of the most successful approaches to describe the physical properties of systems with strong electron-electron correlations such as bulk materials, multi-layers, surfaces, 2D materials and nanostructures in both metallic and insulating phases. Strongly correlated materials usually include partially-filled localized d- or f-orbitals, and DMFT takes into account crucial for these systems time-resolved interaction between electrons when they “meet” on one atom and occupy one of these orbitals. The First Part of the book covers the general formalism of DMFT as a many-body theory, followed by generalizations of the approach on the cases of finite systems and out-of-equilibrium regime. In the last Chapter of the First Part we discuss generalizations of the approach on the case when the non-local interactions are taken into account. The Second Part of the book covers methodologies of merging DMFT with ab initio static Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) approaches. Such combined DFT+DMFT and DMFT+TDDFT computational techniques allow one to include the effects of strong electron-electron correlations at the accurate ab initio level. These tools can be applied to complex multi-atom multi-orbital systems currently not accessible to DMFT. The book helps broad audiences of students and researchers from the theoretical and computational communities of condensed matter physics, material science, and chemistry to become familiar with this state-of-art approach and to use it for reaching a deeper understanding of the properties of strongly correlated systems and for synthesis of new technologically-important materials.
The Study of Two-particle Response Functions in Strongly Correlated Electron Systems Within the Dynamical Mean Field Theory
Author | : Hyowon Park |
Publisher | : |
Total Pages | : 175 |
Release | : 2011 |
Genre | : Correlation (Statistics) |
ISBN | : |
In this thesis, we tackle various problems in strongly correlated electron systems, which can be addressed properly via the non-perturbative dynamical mean field theory (DMFT) approach using the continuous time quantum Monte Carlo method as an impurity solver. First, we revisit the old Nagaoka ferromagnetism problem in the U=oo Hubbard model and study the stability of the ferromagnetic state as a function of the temperature, the doping level, and the next-nearest-neighbor hopping t'. We then address the nature of the Mott transition in the two-dimensional Hubbard model at half-filling using cluster DMFT. Cluster DMFT can incorporate the short-range correlations beyond DMFT by extending the spatial range in which correlations are treated exactly to a finite cluster size. The non-local correlations reduce substantially the critical interaction U and modify the shape of the transition lines in the phase diagram. We then concentrate on the calculation of two-particle response functions from the ab initio perspective by means of computing the one-particle excitation spectrum using the combination of the density functional theory (DFT) and DMFT and extracting the two-particle irreducible vertex function from a local two-particle Green's function computed within DMFT. In particular, we derive the equations for calculating the magnetic/charge susceptibility and the pairing susceptibility in superconductivity. This approach is applied to the Hubbard model and the periodic Anderson model and we determine the phase diagram of magnetism and superconductivity in these models. We show that the superconducting phase is indeed stable near the magnetic phase where the pairing interaction mediated by spin fluctuations is dominantly enhanced. The non-local correlation effect to superconductivity is also discussed using the dual fermion approach and the dynamical vertex approximation. We finally apply the vertex function approach within DFT+DMFT to a Fe-based superconductor, BaFe2As2, and compute the dynamical magnetic susceptibility in this material. Our calculation results show a good agreement with the magnetic excitation spectra observed in a neutron scattering experiment. The response function calculation method derived in this thesis can capture both a localized and an itinerant nature of collective excitations in strongly correlated electron systems.
Lectures on the Physics of Strongly Correlated Systems XII
Author | : Adolfo Avella |
Publisher | : American Institute of Physics |
Total Pages | : 288 |
Release | : 2008-06-05 |
Genre | : Science |
ISBN | : |
The volume contains the lectures delivered at the XII Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2007. The focus of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographies of relevant subjects in the field of Condensed Matter Physics. Contributions include: Quantum Magnetism (Independent spins and Weiss meanfield theory; Finite Heisenberg clusters; Linear spin-wave theory; Classical and quantum Monte Carlo; Entanglement in quantum spin systems); Nanomagnets and Entanglement (The Dynamical Mean Field and Cluster Approximations; Quantum Monte Carlo Algorithms for the Quantum Cluster Problem; Analytic Continuation of Quantum Monte Carlo Data); The Dynamical Cluster Approximation with Quantum Monte Carlo Cluster Solvers (Fermi liquids; Fermi-liquid instabilities at quantum phase transitions: theory; Fermi-liquid instabilities at quantum phase transitions: experiment; Metal-insulator transition in heavily doped semiconductors); Quantum phase transitions; Correlated thermoelectric (Phenomenological equations; Physical interpretation; Solution of transport equations; Linear response theory; Current operators; Mahan-Jonson theorem; Microscopic solution for transport coefficients).
Utilization of Renormalized Mean-Field Theory upon Novel Quantum Materials
Author | : Wei-Lin Tu |
Publisher | : Springer |
Total Pages | : 91 |
Release | : 2019-05-08 |
Genre | : Technology & Engineering |
ISBN | : 981137824X |
This book offers a new approach to the long-standing problem of high-Tc copper-oxide superconductors. It has been demonstrated that starting from a strongly correlated Hamiltonian, even within the mean-field regime, the “competing orders” revealed by experiments can be achieved using numerical calculations. In the introduction, readers will find a brief review of the high-Tc problem and the unique challenges it poses, as well as a comparatively simple numerical approach, the renormalized mean-field theory (RMFT), which provides rich results detailed in the following chapters. With an additional phase picked up by the original Hamiltonian, some behaviors of interactive fermions under an external magnetic field, which have since been experimentally observed using cold atom techniques, are also highlighted.
Modern Theories of Many-Particle Systems in Condensed Matter Physics
Author | : Daniel C. Cabra |
Publisher | : Springer Science & Business Media |
Total Pages | : 380 |
Release | : 2012-01-05 |
Genre | : Technology & Engineering |
ISBN | : 3642104487 |
Condensed matter systems where interactions are strong are inherently difficult to analyze theoretically. The situation is particularly interesting in low-dimensional systems, where quantum fluctuations play a crucial role. Here, the development of non-perturbative methods and the study of integrable field theory have facilitated the understanding of the behavior of many quasi one- and two-dimensional strongly correlated systems. In view of the same rapid development that has taken place for both experimental and numerical techniques, as well as the emergence of novel testing-grounds such as cold atoms or graphene, the current understanding of strongly correlated condensed matter systems differs quite considerably from standard textbook presentations. The present volume of lecture notes aims to fill this gap in the literature by providing a collection of authoritative tutorial reviews, covering such topics as quantum phase transitions of antiferromagnets and cuprate-based high-temperature superconductors, electronic liquid crystal phases, graphene physics, dynamical mean field theory applied to strongly correlated systems, transport through quantum dots, quantum information perspectives on many-body physics, frustrated magnetism, statistical mechanics of classical and quantum computational complexity, and integrable methods in statistical field theory. As both graduate-level text and authoritative reference on this topic, this book will benefit newcomers and more experienced researchers in this field alike.
Emergent Phenomena in Correlated Matter
Author | : Eva Pavarini |
Publisher | : Forschungszentrum Jülich |
Total Pages | : 562 |
Release | : 2013 |
Genre | : |
ISBN | : 3893368841 |
Modern Theories of Many-Particle Systems in Condensed Matter Physics
Author | : Daniel C. Cabra |
Publisher | : Springer Science & Business Media |
Total Pages | : 380 |
Release | : 2012-01-05 |
Genre | : Technology & Engineering |
ISBN | : 3642104495 |
Condensed matter systems where interactions are strong are inherently difficult to analyze theoretically. The situation is particularly interesting in low-dimensional systems, where quantum fluctuations play a crucial role. Here, the development of non-perturbative methods and the study of integrable field theory have facilitated the understanding of the behavior of many quasi one- and two-dimensional strongly correlated systems. In view of the same rapid development that has taken place for both experimental and numerical techniques, as well as the emergence of novel testing-grounds such as cold atoms or graphene, the current understanding of strongly correlated condensed matter systems differs quite considerably from standard textbook presentations. The present volume of lecture notes aims to fill this gap in the literature by providing a collection of authoritative tutorial reviews, covering such topics as quantum phase transitions of antiferromagnets and cuprate-based high-temperature superconductors, electronic liquid crystal phases, graphene physics, dynamical mean field theory applied to strongly correlated systems, transport through quantum dots, quantum information perspectives on many-body physics, frustrated magnetism, statistical mechanics of classical and quantum computational complexity, and integrable methods in statistical field theory. As both graduate-level text and authoritative reference on this topic, this book will benefit newcomers and more experienced researchers in this field alike.
Nanooptics and Photonics, Nanochemistry and Nanobiotechnology, and Their Applications
Author | : Olena Fesenko |
Publisher | : Springer Nature |
Total Pages | : 414 |
Release | : 2020-11-23 |
Genre | : Science |
ISBN | : 3030522687 |
This book highlights some of the latest advances in nanotechnology and nanomaterials from leading researchers in Ukraine, Europe and beyond. It features contributions presented at the 7th International Science and Practice Conference Nanotechnology and Nanomaterials (NANO2019), which was held on August 27–30, 2019 at Lviv Polytechnic National University, and was jointly organized by the Institute of Physics of the National Academy of Sciences of Ukraine, University of Tartu (Estonia), University of Turin (Italy), and Pierre and Marie Curie University (France). Internationally recognized experts from a wide range of universities and research institutions share their knowledge and key findings on material properties, behavior, and synthesis. This book’s companion volume also addresses topics such as nano-optics, energy storage, and biomedical applications.