[PDF] Hubbard Operators In The Theory Of Strongly Correlated Electrons eBook

Author : S. G. Ovchinnikov
Publisher : Imperial College Press
Page : 268 pages
File Size : 30,5 MB
Release : 2004
Category : Science
ISBN : 9781860945977

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This book provides the first systematic discourse on a very peculiarapproach to the theory of strongly correlated systems. HubbardX-operators have been known for a long time but have not been widelyused because of their awkward algebra. The book shows that it ispossible to deal with X-operators even in the general multilevel localeigenstate system, and not just in the case of the nondegenerateHubbard model. X-operators provide the natural language for describingquasiparticles in the Hubbard subbands with unusual doping andtemperature-dependent band structures.

Author : Fabian H L Essler
Publisher : World Scientific
Page : 504 pages
File Size : 19,71 MB
Release : 1994-05-24
Category : Science
ISBN : 981450274X

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Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-Tc 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
Page : 487 pages
File Size : 13,38 MB
Release : 2011-11-01
Category : Science
ISBN : 3642218318

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The volume presents, for the very first time, an exhaustive collection of those modern theoretical 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 materials 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 appreciates 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 : Volodymyr Turkowski
Publisher : Springer Nature
Page : 393 pages
File Size : 18,18 MB
Release : 2021-04-22
Category : Technology & Engineering
ISBN : 3030649040

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​​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.

Author : Adolpho Avella
Publisher : American Inst. of Physics
Page : 380 pages
File Size : 26,1 MB
Release : 2003-08-29
Category : Technology & Engineering
ISBN : 9780735401471

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The objective 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 pedagogical lectures are up-to-date monographs of relevant subjects in the field of condensed matter physics. Contributions include: polarons (the polaron concept, optical properties and internal structure of polarons, many-polaron systems, magnetoabsorption of polarons, optical properties of quantum dots: role of the polaron interaction, interacting polarons in a quantum dot, small polarons); multielectron bubbles in liquid helium: a spherical two-dimensional electron system (oscillation modes, bubble stability and fissioning, the spherical two-dimensional electron gas, the Wigner solid of electrons in the bubble); the numerical approach to the correlated electron problem: quantum Monte Carlo methods (the world line approach for the XXZ model and relation to the 6-vertex model, auxiliary field Quantum Monte Carlo algorithms, application of the auxiliary field QMC to specific Hamiltonians, the Hirsch-Fye impurity algorithm); basic models in the quantum theory of magnetism (the Heisenberg model, the Hubbard model, and the sd-model).

Author : Peter Fulde
Publisher : World Scientific
Page : 550 pages
File Size : 19,37 MB
Release : 2012-08-08
Category : Science
ISBN : 9814397229

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An understanding of the effects of electronic correlations in quantum systems is one of the most challenging problems in physics, partly due to the relevance in modern high technology. Yet there exist hardly any books on the subject which try to give a comprehensive overview on the field covering insulators, semiconductors, as well as metals. The present book tries to fill that gap.It intends to provide graduate students and researchers a comprehensive survey of electron correlations, weak and strong, in insulators, semiconductors and metals. This topic is a central one in condensed matter and beyond that in theoretical physics. The reader will have a better understanding of the great progress which has been made in the field over the past few decades.

Author : G Baskaran
Publisher : World Scientific
Page : 444 pages
File Size : 10,13 MB
Release : 1991-02-28
Category : Science
ISBN : 9814569348

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This is the second in a series of miniworkshops and Adriatico conferences devoted to the exciting field of strongly correlated electron systems including quantum Hall effect, metal insulator transition, heavy fermions and high Tc superconductivity. In spite of enormous efforts made by physicists worldwide to solve these difficult problems, many important issues are still widely open and this topic remains the most active field in condensed matter physics. The review talks and reports on original research given by the experts in the field represent a state-of-the-art summary of this fast-moving field.

Author : Anatoly G. Kusraev
Publisher : Springer Nature
Page : 337 pages
File Size : 26,42 MB
Release : 2021-01-13
Category : Mathematics
ISBN : 3030497631

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This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July 2019. Intended for mathematicians specializing in operator theory, functional spaces, differential equations or mathematical modeling, the book provides a state-of-the-art account of various fascinating areas of operator theory, ranging from various classes of operators (positive operators, convolution operators, backward shift operators, singular and fractional integral operators, partial differential operators) to important applications in differential equations, inverse problems, approximation theory, metric theory of surfaces, the Hubbard model, social stratification models, and viscid incompressible fluids.

Author : Dionys Baeriswyl
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 20,68 MB
Release : 2013-11-11
Category : Science
ISBN : 1489910425

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In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).