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Cover: 9781461269281 | Interacting Electrons and Quantum Magnetism | Assa Auerbach | Buch
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Interacting Electrons and Quantum Magnetism
Taschenbuch von Assa Auerbach
Sprache: Englisch

58,95 €*

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Beschreibung
In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner­ ant magnets, and superconductors. It is in essence a weak coupling expan­ sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high­ temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con­ strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha­ miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.
In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner­ ant magnets, and superconductors. It is in essence a weak coupling expan­ sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high­ temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con­ strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha­ miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.
Zusammenfassung
This book emphasizes the role that electron interactions play in the properties of condensed matter. It teaches the use of the powerful nonperturbative techniques that have become available in the last decades to discuss such topics as mixed valence systems, Kondo systems, heavy electrons, high-temperature copper oxide superconductors, the quantum Hall effect, and low-dimensional isotropic magnets.
Inhaltsverzeichnis
I Basic Models.- 1 Electron Interactions in Solids.- 2 Spin Exchange.- 3 The Hubbard Model and Its Descendants.- II Wave Functions and Correlations.- 4 Ground States of the Hubbard Model.- 5 Ground States of the Heisenberg Model.- 6 Disorder in Low Dimensions.- 7 Spin Representations.- 8 Variational Wave Functions and Parent Hamiltonians.- 9 From Ground States to Excitations.- III Path Integral Approximations.- 10 The Spin Path Integral.- 11 Spin Wave Theory.- 12 The Continuum Approximation.- 13 Nonlinear Sigma Model: Weak Coupling.- 14 The Nonlinear Sigma Model: Large N.- 15 Quantum Antiferromagnets: Continuum Results.- 16 SU(N) Heisenberg Models.- 17 The Large N Expansion.- 18 Schwinger Bosons Mean Field Theory.- 19 The Semiclassical Theory of the t - J Model.- IV Mathematical Appendices.- Appendix A Second Quantization.- A.1 Fock States.- A.2 Normal Bilinear Operators.- A.3 Noninteracting Hamiltonians.- A.4 Exercises.- Appendix B Linear Response and Generating Functionals.- B.1 Spin Response Function.- B.2 Fluctuations and Dissipation.- B.3 The Generating Functional.- Appendix C Bose and Fermi Coherent States.- C.1 Complex Integration.- C.2 Grassmann Variables.- C.3 Coherent States.- C.4 Exercises.- Appendix D Coherent State Path Integrals.- D.1 Constructing the Path Integral.- D.2 Normal Bilinear Hamiltonians.- D.3 Matsubara Representation.- D.4 Matsubara Sums.- D.5 Exercises.- Appendix E The Method of Steepest Descents.
Details
Medium: Taschenbuch
Seiten: 272
Reihe: Graduate Texts in Contemporary Physics
Inhalt: xiii
255 S.
ISBN-13: 9781461269281
ISBN-10: 1461269288
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Auerbach, Assa
Auflage: Softcover reprint of the original 1st ed. 1994
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Contemporary Physics
Maße: 235 x 155 x 15 mm
Von/Mit: Assa Auerbach
Erscheinungsdatum: 06.10.2012
Gewicht: 0,417 kg
preigu-id: 106118763
Zusammenfassung
This book emphasizes the role that electron interactions play in the properties of condensed matter. It teaches the use of the powerful nonperturbative techniques that have become available in the last decades to discuss such topics as mixed valence systems, Kondo systems, heavy electrons, high-temperature copper oxide superconductors, the quantum Hall effect, and low-dimensional isotropic magnets.
Inhaltsverzeichnis
I Basic Models.- 1 Electron Interactions in Solids.- 2 Spin Exchange.- 3 The Hubbard Model and Its Descendants.- II Wave Functions and Correlations.- 4 Ground States of the Hubbard Model.- 5 Ground States of the Heisenberg Model.- 6 Disorder in Low Dimensions.- 7 Spin Representations.- 8 Variational Wave Functions and Parent Hamiltonians.- 9 From Ground States to Excitations.- III Path Integral Approximations.- 10 The Spin Path Integral.- 11 Spin Wave Theory.- 12 The Continuum Approximation.- 13 Nonlinear Sigma Model: Weak Coupling.- 14 The Nonlinear Sigma Model: Large N.- 15 Quantum Antiferromagnets: Continuum Results.- 16 SU(N) Heisenberg Models.- 17 The Large N Expansion.- 18 Schwinger Bosons Mean Field Theory.- 19 The Semiclassical Theory of the t - J Model.- IV Mathematical Appendices.- Appendix A Second Quantization.- A.1 Fock States.- A.2 Normal Bilinear Operators.- A.3 Noninteracting Hamiltonians.- A.4 Exercises.- Appendix B Linear Response and Generating Functionals.- B.1 Spin Response Function.- B.2 Fluctuations and Dissipation.- B.3 The Generating Functional.- Appendix C Bose and Fermi Coherent States.- C.1 Complex Integration.- C.2 Grassmann Variables.- C.3 Coherent States.- C.4 Exercises.- Appendix D Coherent State Path Integrals.- D.1 Constructing the Path Integral.- D.2 Normal Bilinear Hamiltonians.- D.3 Matsubara Representation.- D.4 Matsubara Sums.- D.5 Exercises.- Appendix E The Method of Steepest Descents.
Details
Medium: Taschenbuch
Seiten: 272
Reihe: Graduate Texts in Contemporary Physics
Inhalt: xiii
255 S.
ISBN-13: 9781461269281
ISBN-10: 1461269288
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Auerbach, Assa
Auflage: Softcover reprint of the original 1st ed. 1994
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Contemporary Physics
Maße: 235 x 155 x 15 mm
Von/Mit: Assa Auerbach
Erscheinungsdatum: 06.10.2012
Gewicht: 0,417 kg
preigu-id: 106118763
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