Exactly Solvable Models of Strongly Correlated Electrons

Exactly Solvable Models of Strongly Correlated Electrons

Author: Vladimir E. Korepin

Publisher: World Scientific

Published: 1994

Total Pages: 506

ISBN-13: 9789810215347

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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-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.


Book Synopsis Exactly Solvable Models of Strongly Correlated Electrons by : Vladimir E. Korepin

Download or read book Exactly Solvable Models of Strongly Correlated Electrons written by Vladimir E. Korepin and published by World Scientific. This book was released on 1994 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Infinite-dimensional Algebras in Exactly Solvable Models of Strongly Correlated Electrons and Statistical Mechanics

Infinite-dimensional Algebras in Exactly Solvable Models of Strongly Correlated Electrons and Statistical Mechanics

Author: Denis Uglov

Publisher:

Published: 1995

Total Pages: 250

ISBN-13:

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Book Synopsis Infinite-dimensional Algebras in Exactly Solvable Models of Strongly Correlated Electrons and Statistical Mechanics by : Denis Uglov

Download or read book Infinite-dimensional Algebras in Exactly Solvable Models of Strongly Correlated Electrons and Statistical Mechanics written by Denis Uglov and published by . This book was released on 1995 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hubbard Operators in the Theory of Strongly Correlated Electrons

Hubbard Operators in the Theory of Strongly Correlated Electrons

Author: S. G. Ovchinnikov

Publisher: Imperial College Press

Published: 2004

Total Pages: 268

ISBN-13: 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.


Book Synopsis Hubbard Operators in the Theory of Strongly Correlated Electrons by : S. G. Ovchinnikov

Download or read book Hubbard Operators in the Theory of Strongly Correlated Electrons written by S. G. Ovchinnikov and published by Imperial College Press. This book was released on 2004 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theoretical Methods for Strongly Correlated Electrons

Theoretical Methods for Strongly Correlated Electrons

Author: David Sénéchal

Publisher: Springer Science & Business Media

Published: 2004

Total Pages: 370

ISBN-13: 0387008950

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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. Taken together, the contributions to this volume represent a comprehensive overview of current problems and developments.


Book Synopsis Theoretical Methods for Strongly Correlated Electrons by : David Sénéchal

Download or read book Theoretical Methods for Strongly Correlated Electrons written by David Sénéchal and published by Springer Science & Business Media. This book was released on 2004 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Taken together, the contributions to this volume represent a comprehensive overview of current problems and developments.

Finite Size Effects in Correlated Electron Models

Finite Size Effects in Correlated Electron Models

Author: Andrei A. Zvyagin

Publisher: World Scientific

Published: 2005

Total Pages: 380

ISBN-13: 1860945031

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The book presents exact results for one-dimensional models (including quantum spin models) of strongly correlated electrons in a comprehensive and concise manner. It incorporates important results related to magnetic and hybridization impurities in electron hosts and contains exact original results for disordered ensembles of impurities in interacting systems. These models describe a number of real low-dimensional electron systems that are widely used in nanophysics and microelectronics.An important method of modern theoretical and mathematical physics — the Bethe's Ansatz (BA) — is introduced to readers. This book presents different forms of the BA for periodic and open quantum chains. Other forms dealt with are the co-ordinate BA, thermodynamic BA, nested BA, algebraic BA, and thermal BA. The book also contains a compact description of other theoretical methods such as scaling, conformal field theory, Abelian and non-Abelian bosonizations.The book is suitable for use as a textbook by graduate students in non-perturbative methods of low-dimensional quantum many-body theory. It will also be a useful source of reference for qualified physicists, as well as non-experts in low-dimensional physics, as it explores material necessary for further studies in the fields of exactly solvable quantum models and low-dimensional correlated electron systems.


Book Synopsis Finite Size Effects in Correlated Electron Models by : Andrei A. Zvyagin

Download or read book Finite Size Effects in Correlated Electron Models written by Andrei A. Zvyagin and published by World Scientific. This book was released on 2005 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents exact results for one-dimensional models (including quantum spin models) of strongly correlated electrons in a comprehensive and concise manner. It incorporates important results related to magnetic and hybridization impurities in electron hosts and contains exact original results for disordered ensembles of impurities in interacting systems. These models describe a number of real low-dimensional electron systems that are widely used in nanophysics and microelectronics.An important method of modern theoretical and mathematical physics — the Bethe's Ansatz (BA) — is introduced to readers. This book presents different forms of the BA for periodic and open quantum chains. Other forms dealt with are the co-ordinate BA, thermodynamic BA, nested BA, algebraic BA, and thermal BA. The book also contains a compact description of other theoretical methods such as scaling, conformal field theory, Abelian and non-Abelian bosonizations.The book is suitable for use as a textbook by graduate students in non-perturbative methods of low-dimensional quantum many-body theory. It will also be a useful source of reference for qualified physicists, as well as non-experts in low-dimensional physics, as it explores material necessary for further studies in the fields of exactly solvable quantum models and low-dimensional correlated electron systems.

Off-Diagonal Bethe Ansatz for Exactly Solvable Models

Off-Diagonal Bethe Ansatz for Exactly Solvable Models

Author: Yupeng Wang

Publisher: Springer

Published: 2015-04-21

Total Pages: 303

ISBN-13: 3662467569

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This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.


Book Synopsis Off-Diagonal Bethe Ansatz for Exactly Solvable Models by : Yupeng Wang

Download or read book Off-Diagonal Bethe Ansatz for Exactly Solvable Models written by Yupeng Wang and published by Springer. This book was released on 2015-04-21 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.

The One-Dimensional Hubbard Model

The One-Dimensional Hubbard Model

Author: Fabian H. L. Essler

Publisher: Cambridge University Press

Published: 2005-02-07

Total Pages: 692

ISBN-13: 1139441582

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This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.


Book Synopsis The One-Dimensional Hubbard Model by : Fabian H. L. Essler

Download or read book The One-Dimensional Hubbard Model written by Fabian H. L. Essler and published by Cambridge University Press. This book was released on 2005-02-07 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.

Strongly Correlated Systems, Coherence And Entanglement

Strongly Correlated Systems, Coherence And Entanglement

Author: J M P Carmelo

Publisher: World Scientific

Published: 2007-07-12

Total Pages: 612

ISBN-13: 9814475831

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This volume presents a collection of review papers on recent work in the connected areas of strongly correlated systems, the effects of coherence on macroscopic systems, and entanglement in quantum systems. These areas have attracted considerable interest due to their complexity and associated unexpected nontrivial phenomena, and also due to their potential applications in various fields, from materials science to information technology. The coverage includes strongly correlated electronic systems such as low-dimensional complex materials, ordered and disordered spin systems, and aspects of the physics of manganites and graphene, both in equilibrium and far from equilibrium.


Book Synopsis Strongly Correlated Systems, Coherence And Entanglement by : J M P Carmelo

Download or read book Strongly Correlated Systems, Coherence And Entanglement written by J M P Carmelo and published by World Scientific. This book was released on 2007-07-12 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of review papers on recent work in the connected areas of strongly correlated systems, the effects of coherence on macroscopic systems, and entanglement in quantum systems. These areas have attracted considerable interest due to their complexity and associated unexpected nontrivial phenomena, and also due to their potential applications in various fields, from materials science to information technology. The coverage includes strongly correlated electronic systems such as low-dimensional complex materials, ordered and disordered spin systems, and aspects of the physics of manganites and graphene, both in equilibrium and far from equilibrium.

Finite Size Effects in Correlated Electron Models

Finite Size Effects in Correlated Electron Models

Author: Andrei A. Zvyagin

Publisher: World Scientific

Published: 2005

Total Pages: 380

ISBN-13: 1860945031

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The book presents exact results for one-dimensional models (including quantum spin models) of strongly correlated electrons in a comprehensive and concise manner. It incorporates important results related to magnetic and hybridization impurities in electron hosts and contains exact original results for disordered ensembles of impurities in interacting systems. These models describe a number of real low-dimensional electron systems that are widely used in nanophysics and microelectronics.An important method of modern theoretical and mathematical physics — the Bethe's Ansatz (BA) — is introduced to readers. This book presents different forms of the BA for periodic and open quantum chains. Other forms dealt with are the co-ordinate BA, thermodynamic BA, nested BA, algebraic BA, and thermal BA. The book also contains a compact description of other theoretical methods such as scaling, conformal field theory, Abelian and non-Abelian bosonizations.The book is suitable for use as a textbook by graduate students in non-perturbative methods of low-dimensional quantum many-body theory. It will also be a useful source of reference for qualified physicists, as well as non-experts in low-dimensional physics, as it explores material necessary for further studies in the fields of exactly solvable quantum models and low-dimensional correlated electron systems.


Book Synopsis Finite Size Effects in Correlated Electron Models by : Andrei A. Zvyagin

Download or read book Finite Size Effects in Correlated Electron Models written by Andrei A. Zvyagin and published by World Scientific. This book was released on 2005 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents exact results for one-dimensional models (including quantum spin models) of strongly correlated electrons in a comprehensive and concise manner. It incorporates important results related to magnetic and hybridization impurities in electron hosts and contains exact original results for disordered ensembles of impurities in interacting systems. These models describe a number of real low-dimensional electron systems that are widely used in nanophysics and microelectronics.An important method of modern theoretical and mathematical physics — the Bethe's Ansatz (BA) — is introduced to readers. This book presents different forms of the BA for periodic and open quantum chains. Other forms dealt with are the co-ordinate BA, thermodynamic BA, nested BA, algebraic BA, and thermal BA. The book also contains a compact description of other theoretical methods such as scaling, conformal field theory, Abelian and non-Abelian bosonizations.The book is suitable for use as a textbook by graduate students in non-perturbative methods of low-dimensional quantum many-body theory. It will also be a useful source of reference for qualified physicists, as well as non-experts in low-dimensional physics, as it explores material necessary for further studies in the fields of exactly solvable quantum models and low-dimensional correlated electron systems.

Strongly Correlated Electron Systems Ii - Proceedings Of The Adriatico Conference And Miniworkshop

Strongly Correlated Electron Systems Ii - Proceedings Of The Adriatico Conference And Miniworkshop

Author: G Baskaran

Publisher: World Scientific

Published: 1991-02-28

Total Pages: 444

ISBN-13: 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.


Book Synopsis Strongly Correlated Electron Systems Ii - Proceedings Of The Adriatico Conference And Miniworkshop by : G Baskaran

Download or read book Strongly Correlated Electron Systems Ii - Proceedings Of The Adriatico Conference And Miniworkshop written by G Baskaran and published by World Scientific. This book was released on 1991-02-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.