Interacting electrons and quantum magnetism:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1994
|
| Schriftenreihe: | Graduate texts in contemporary physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 255 S. Ill., graph. Darst. |
| ISBN: | 3540942866 0387942866 |
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Datensatz im Suchindex
| _version_ | 1820595283983073280 |
|---|---|
| adam_text |
ASSA AUERBACH
INTERACTING ELECTRONS AND
QUANTUM
MAGNETISM
WITH 34 ILLUSTRATIONS
SPRINGER-VERLAG
NEW
YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO
HONG KONG BARCELONA BUDAPEST
CONTENTS
PREFACE VII
I BASIC MODELS
1
1 ELECTRON INTERACTIONS
IN
SOLIDS
3
1.1
SINGLE ELECTRON THEORY
3
1.2
FIELDS
AND
INTERACTIONS
4
1.3
MAGNITUDE
OF
INTERACTIONS
IN
METALS
6
1.4
EFFECTIVE MODELS
7
1.5
EXERCISES
8
2 SPIN EXCHANGE
"
11
2.1
FERROMAGNETIC EXCHANGE
11
2.2 ANTIFERROMAGNETIC EXCHANGE
13
2.3 SUPEREXCHANGE
16
2.4 EXERCISES
19
3
THE
HUBBARD MODEL
AND ITS
DESCENDANTS
21
3.1 TRUNCATING
THE
INTERACTIONS
22
3.2
AT
LARGE
U:
THE
T-J
MODEL
25
3.3
THE
NEGATIVE-*/ MODEL
28
3.3.1
THE
PSEUDO-SPIN MODEL
AND
SUPERCONDUCTIVITY
.
.
. 30
3.4
EXERCISES
33
II WAVE FUNCTIONS
AND
CORRELATIONS
37
4 GROUND STATES OF THE HUBBARD MODEL 39
4.1 VARIATIONAL MAGNETIC STATES 40
4.2 SOME GROUND STATE THEOREMS 45
4.3 EXERCISES 48
5 GROUND STATES OF THE HEISENBERG MODEL 51
5.1 THE ANTIFERROMAGNET 52
5.2 HALF-ODD INTEGER SPIN CHAINS 56
X CONTENTS
5.3 EXERCISES 59
6 DISORDER IN LOW DIMENSIONS 61
6.1 SPONTANEOUSLY BROKEN SYMMETRY 61
6.2 MERMIN AND WAGNER'S THEOREM 62
6.3 QUANTUM DISORDER AT
T -
0 66
6.4
EXERCISES 68
7 SPIN REPRESENTATIONS 69
7.1 HOLSTEIN-PRIMAKOFF BOSONS 69
7.2 SCHWINGER BOSONS 70
7.2.1 SPIN ROTATIONS 72
7.3 SPIN COHERENT STATES 72
7.3.1 THE
6
INTEGRALS 75
7.4 EXERCISES 75
8 VARIATIONAL WAVE FUNCTIONS AND PARENT HAMILTONIANS 79
8.1
VALENCE BOND STATES 79
8.2
S
=
\
STATES 81
8.2.1 THE MAJUMDAR-GHOSH HAMILTONIAN 83
8.2.2 SQUARE LATTICE RVB STATES 84
8.3 VALENCE BOND SOLIDS AND AKLT MODELS 85
8.3.1 CORRELATIONS IN VALENCE BOND SOLIDS 87
8.4 EXERCISES 88
9 FROM GROUND STATES TO EXCITATIONS 93
9.1 THE SINGLE MODE APPROXIMATION 94
9.2 GOLDSTONE MODES _. . 95
9.3 THE HALDANE GAP AND THE SMA 96
III PATH INTEGRAL APPROXIMATIONS 99
10 THE SPIN PATH INTEGRAL 101
10.1 CONSTRUCTION OF THE PATH INTEGRAL 101
10.1.1 THE GREEN'S FUNCTION 105
10.2 THE LARGE
S
EXPANSION 106
10.2.1 SEMICLASSICAL DYNAMICS 107
10.2.2 SEMICLASSICAL SPECTRUM 109
10.3 EXERCISES 110
11 SPIN WAVE THEORY 113
11.1 SPIN WAVES: PATH INTEGRAL APPROACH 113
11.1.1 THE FERROMAGNET 118
11.1.2 THE ANTIFERROMAGNET 119
11.2 SPIN WAVES: HOLSTEIN-PRIMAKOFF APPROACH 120
CONTENTS XI
11.2.1 THE FERROMAGNET 121
11.2.2 THE ANTIFERROMAGNET 123
11.3 EXERCISES 126
12 THE CONTINUUM APPROXIMATION 129
12.1 HALDANE'S MAPPING 130
12.2 THE CONTINUUM HAMILTONIAN 131
12.3 THE KINETIC TERM 133
12.4 PARTITION FUNCTION AND CORRELATIONS 133
12.5 EXERCISES 136
13 NONLINEAR SIGMA MODEL: WEAK COUPLING 139
13.1 THE LATTICE REGULARIZATION 139
13.2 WEAK COUPLING EXPANSION 141
13.3 POOR MAN'S RENORMALIZATION 142
13.4 THE
0
FUNCTION 147
13.5 EXERCISES 150
14 THE NONLINEAR SIGMA MODEL: LARGE
N
153
14.1
THE
CP
1
FORMULATION 153
14.2
CP
N
-
X
MODELS AT LARGE
N
155
14.3 EXERCISES 157
15 QUANTUM ANTIFERROMAGNETS: CONTINUUM RESULTS 159
15.1
ONE DIMENSION, THE 0 TERM 159
15.2 ONE DIMENSION, INTEGER SPINS 162
15.3 TWO DIMENSIONS 163
16
SU(AT)
HEISENBERG MODELS 165
16.1 FERROMAGNET, SCHWINGER BOSONS 166
16.2 ANTIFERROMAGNET, SCHWINGER BOSONS 167
16.3 ANTIFERROMAGNET, CONSTRAINED FERMIONS 168
16.4 THE GENERATING FUNCTIONAL 7 169
16.5 THE HUBBARD-STRATONOVICH TRANSFORMATION 171
16.6
CORRELATION FUNCTIONS 172
17 THE LARGE
N
EXPANSION 175
17.1 FLUCTUATIONS AND GAUGE FIELDS 176
17.2 I/AT EXPANSION DIAGRAMS 178
17.3 SUM RULES 181
17.3.1 ABSENCE OF CHARGE FLUCTUATIONS 182
17.3.2 ON-SITE SPIN FLUCTUATIONS 183
17.4 EXERCISES 186
XII CONTENTS
18 SCHWINGER BOSONS MEAN FIELD THEORY 187
18.1 THE CASE OF THE FERROMAGNET 187
18.1.1 ONE DIMENSION 191
18.1.2 TWO DIMENSIONS 192
18.2 THE CASE OF THE ANTIFERROMAGNET 194
18.2.1 LONG-RANGE ANTIFERROMAGNETIC ORDER 198
18.2.2
ONE DIMENSION 200
18.2.3 TWO DIMENSIONS 201
18.3 EXERCISES 203
19 THE SEMICLASSICAL THEORY OF THE
T-J
MODEL 205
19.1
SCHWINGER BOSONS AND SLAVE FERMIONS 206
19.2 SPIN-HOLE COHERENT STATES 207
19.3 THE CLASSICAL THEORY: SMALL POLARONS 211
19.4 POLARON DYNAMICS AND SPIN TUNNELING 214
19.5 THE
T'
-
J
MODEL 218
19.5.1 SUPERCONDUCTIVITY? 220
19.6 EXERCISES 221
IV MATHEMATICAL APPENDICES 223
APPENDIX A
SECOND
QUANTIZATION
-
225
A.I
FOCK STATES 225
A.2 NORMAL BILINEAR OPERATORS 226
A.3 NONINTERACTING HAMILTONIANS 227
A.4 EXERCISES 228
APPENDIX B
LINEAR
RESPONSE AND GENERATING FUNCTIONALS 231
B.I
SPIN RESPONSE FUNCTION 231
B.2 FLUCTUATIONS AND DISSIPATION 233
B.3 THE GENERATING FUNCTIONAL _ 233
APPENDIX C
BOSE
AND FERMI COHERENT STATES 237
C.I COMPLEX INTEGRATION 237
C.2 GRASSMANN VARIABLES 237
C.3 COHERENT STATES 239
C.4 EXERCISES 240
APPENDIX D
COHERENT
STATE PATH INTEGRALS 241
D.I CONSTRUCTING THE PATH.INTEGRAL 241
D.2 NORMAL BILINEAR HAMILTONIANS 242
D.3 MATSUBARA REPRESENTATION 244
D.4 MATSUBARA SUMS 244
D.5 EXERCISES
APPENDIX E
THE
METHOD OF STEEPEST DESCENTS
INDEX
CONTENTS
XIII
246
249
253 |
| any_adam_object | 1 |
| author | Auerbach, Assa |
| author_facet | Auerbach, Assa |
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| dewey-search | 530.4/12 |
| dewey-sort | 3530.4 212 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV009620322 |
| illustrated | Illustrated |
| indexdate | 2025-01-07T13:02:41Z |
| institution | BVB |
| isbn | 3540942866 0387942866 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006358300 |
| oclc_num | 30028928 |
| open_access_boolean | |
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| physical | XIII, 255 S. Ill., graph. Darst. |
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| record_format | marc |
| series2 | Graduate texts in contemporary physics |
| spelling | Auerbach, Assa Verfasser aut Interacting electrons and quantum magnetism Assa Auerbach New York [u.a.] Springer 1994 XIII, 255 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in contemporary physics Electron-electron interactions Energy-band theory of solids Magnetism Path integrals Wave functions Elektronenkorrelation (DE-588)4210527-4 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf Starke Kopplung (DE-588)4382353-1 gnd rswk-swf Bändermodell (DE-588)4143892-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Elektron-Elektron-Wechselwirkung (DE-588)4151859-7 gnd rswk-swf Bändermodell (DE-588)4143892-9 s Elektron-Elektron-Wechselwirkung (DE-588)4151859-7 s DE-604 Festkörper (DE-588)4016918-2 s Elektronenkorrelation (DE-588)4210527-4 s Starke Kopplung (DE-588)4382353-1 s Mathematisches Modell (DE-588)4114528-8 s Pfadintegral (DE-588)4173973-5 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-0869-3 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358300&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Auerbach, Assa Interacting electrons and quantum magnetism Electron-electron interactions Energy-band theory of solids Magnetism Path integrals Wave functions Elektronenkorrelation (DE-588)4210527-4 gnd Pfadintegral (DE-588)4173973-5 gnd Festkörper (DE-588)4016918-2 gnd Starke Kopplung (DE-588)4382353-1 gnd Bändermodell (DE-588)4143892-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Elektron-Elektron-Wechselwirkung (DE-588)4151859-7 gnd |
| subject_GND | (DE-588)4210527-4 (DE-588)4173973-5 (DE-588)4016918-2 (DE-588)4382353-1 (DE-588)4143892-9 (DE-588)4114528-8 (DE-588)4151859-7 |
| title | Interacting electrons and quantum magnetism |
| title_auth | Interacting electrons and quantum magnetism |
| title_exact_search | Interacting electrons and quantum magnetism |
| title_full | Interacting electrons and quantum magnetism Assa Auerbach |
| title_fullStr | Interacting electrons and quantum magnetism Assa Auerbach |
| title_full_unstemmed | Interacting electrons and quantum magnetism Assa Auerbach |
| title_short | Interacting electrons and quantum magnetism |
| title_sort | interacting electrons and quantum magnetism |
| topic | Electron-electron interactions Energy-band theory of solids Magnetism Path integrals Wave functions Elektronenkorrelation (DE-588)4210527-4 gnd Pfadintegral (DE-588)4173973-5 gnd Festkörper (DE-588)4016918-2 gnd Starke Kopplung (DE-588)4382353-1 gnd Bändermodell (DE-588)4143892-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Elektron-Elektron-Wechselwirkung (DE-588)4151859-7 gnd |
| topic_facet | Electron-electron interactions Energy-band theory of solids Magnetism Path integrals Wave functions Elektronenkorrelation Pfadintegral Festkörper Starke Kopplung Bändermodell Mathematisches Modell Elektron-Elektron-Wechselwirkung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358300&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT auerbachassa interactingelectronsandquantummagnetism |