An introduction to quantum spin systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg ; Dordrecht ; London ; New York
Springer
[2010]
|
| Schriftenreihe: | Lecture notes in physics
816 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 154 Seiten Diagramme |
| ISBN: | 9783642132896 |
Internformat
MARC
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| 100 | 1 | |a Parkinson, John B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to quantum spin systems |c John B. Parkinson, Damian J.J. Farnell |
| 264 | 1 | |a Heidelberg ; Dordrecht ; London ; New York |b Springer |c [2010] | |
| 300 | |a xi, 154 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in physics |v 816 | |
| 650 | 0 | 7 | |a Quantenspinsystem |0 (DE-588)4609091-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenspinsystem |0 (DE-588)4609091-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Farnell, Damian J. J. |e Verfasser |0 (DE-588)142611344 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-642-13290-2 |
| 830 | 0 | |a Lecture notes in physics |v 816 |w (DE-604)BV000003166 |9 816 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020668329 | ||
Datensatz im Suchindex
| _version_ | 1804143413590753280 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 1
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 5
2 SPIN MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 7
2.1 SPIN ANGULAR MOMENTUM . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 7
2.2 COUPLED SPINS . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 10
2.3 TWO INTERACTING SPIN- 12 S . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 11
2.4 COMMUTATORS AND QUANTUM NUMBERS . . . . . . . . . . . . . . . . . .
. . . . . . . 14
2.5 PHYSICAL PICTURE . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 16
2.6 INF INITE ARRAYS OF SPINS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 16
2.7 1D HEISENBERG CHAIN WITH S = 12 AND NEAREST-NEIGHBOUR INTERACTION .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 18
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 19
3 QUANTUM TREATMENT OF THE SPIN- 1 2 CHAIN . . . . . . . . . . . . . . .
. . . . . . . . . . 21
3.1 GENERAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 21
3.2 ALIGNED STATE . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 22
3.3 SINGLE DEVIATION STATES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 23
3.4 TWO DEVIATION STATES. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 27
3.4.1 FORM OF THE STATES . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 33
3.5 THREE DEVIATION STATES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 36
3.5.1 BETHE ANSATZ FOR S Z T = N 2 * 3 . . . . . . . . . . . . . . . . .
. . . . . . 36
3.6 STATES WITH AN ARBITRARY NUMBER OF DEVIATIONS . . . . . . . . . . .
. . . . . . 37
REFERENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 38
4 THE ANTIFERROMAGNETIC GROUND STATE . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 39
4.1 THE FUNDAMENTAL INTEGRAL EQUATION. . . . . . . . . . . . . . . . . .
. . . . . . . . . 39
4.2 SOLUTION OF THE FUNDAMENTAL INTEGRAL EQUATION . . . . . . . . . . .
. . . . . . 43
4.3 THE GROUND STATE ENERGY . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 45
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 47
IX
IMAGE 2
X CONTENTS
5 ANTIFERROMAGNETIC SPIN WAVES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 49
5.1 THE BASIC FORMALISM . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 49
5.2 MAGNETIC FIELD BEHAVIOUR . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 57
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 59
6 THE XY MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 61
6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 61
6.2 CHANGE FROM SPIN OPERATORS TO FERMION OPERATORS . . . . . . . . . .
. . . 62
6.3 FOURIER TRANSFORM . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 68
6.4 QUASIPARTICLE OPERATORS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 69
6.5 QUASIPARTICLE ENERGIES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 71
6.6 GROUND STATE ENERGY OF THE XY-MODEL . . . . . . . . . . . . . . . .
. . . . . . . . 73
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 75
7 SPIN-WAVE THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 77
7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 77
7.2 FERROMAGNETIC SPIN-WAVE THEORY . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 80
7.3 ANTIFERROMAGNETIC SPIN-WAVE THEORY. . . . . . . . . . . . . . . . .
. . . . . . . . 82
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 88
8 NUMERICAL FINITE-SIZE CALCULATIONS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 89
8.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 89
8.2 A SIMPLE EXAMPLE. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 90
8.3 RESULTS IN 1D . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 92
8.4 RESULTS IN 2D . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 95
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 96
9 OTHER APPROXIMATE METHODS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 99
9.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 99
9.2 VARIATIONAL METHOD . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 99
9.3 VARIATIONAL MONTE CARLO METHOD . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 101
9.4 THE GREEN FUNCTION MONTE CARLO METHOD . . . . . . . . . . . . . . .
. . . . . . 104
9.5 PERTURBATION THEORY. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 105
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 108
10 THE COUPLED CLUSTER METHOD . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 109
10.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 109
10.2 THE CCM FORMALISM . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 110
10.3 THE XXZ-MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 115
10.3.1 THE LSUB2 APPROXIMATION FOR THE SPIN-HALF, SQUARE-LATTICE
XXZ-MODEL FOR THE Z-ALIGNED MODEL STATE . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 117
IMAGE 3
CONTENTS XI
10.3.2 THE SUB2 APPROXIMATION FOR THE SPIN-HALF, SQUARE-LATTICE
XXZ-MODEL OF THE Z -ALIGNED MODEL STATE . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 122
10.3.3 HIGH-ORDER CCM CALCULATIONS USING A COMPUTATIONAL APPROACH . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 125
10.3.4 EXCITATION SPECTRUM OF THE SPIN-HALF SQUARE-LATTICE XXZ-MODEL FOR
THE Z -ALIGNED MODEL STATE . . . . . . . . . . . . 127 10.4 THE LATTICE
MAGNETISATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 129
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 134
11 QUANTUM MAGNETISM . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 135
11.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 135
11.2 ONE-DIMENSIONAL MODELS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 136
11.2.1 THE SPIN-HALF J 1 - J 2 MODEL ON THE LINEAR CHAIN . . . . . . . .
136 11.2.2 THE S = 1 HEISENBERG MODEL ON THE LINEAR CHAIN . . . . . . .
138 11.2.3 THE S = 1 HEISENBERG-BIQUADRATIC MODEL ON THE LINEAR CHAIN .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 139
11.3 THE S = 1 / 2 HEISENBERG MODEL FOR ARCHIMEDEAN LATTICES. . . . . .
. . 140 11.4 SPIN PLATEAUX . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 145
11.5 THE SPIN-HALF J 1 - J 2 MODEL ON THE SQUARE LATTICE . . . . . . . .
. . . . . . 146
11.6 THE SHASTRY-SUTHERLAND ANTIFERROMAGNET . . . . . . . . . . . . . .
. . . . . . . . 147
11.7 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 149
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 150
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
|
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| id | DE-604.BV036751069 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:47:16Z |
| institution | BVB |
| isbn | 9783642132896 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020668329 |
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| physical | xi, 154 Seiten Diagramme |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Parkinson, John B. Verfasser aut An introduction to quantum spin systems John B. Parkinson, Damian J.J. Farnell Heidelberg ; Dordrecht ; London ; New York Springer [2010] xi, 154 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 816 Quantenspinsystem (DE-588)4609091-5 gnd rswk-swf Quantenspinsystem (DE-588)4609091-5 s DE-604 Farnell, Damian J. J. Verfasser (DE-588)142611344 aut Erscheint auch als Online-Ausgabe 978-3-642-13290-2 Lecture notes in physics 816 (DE-604)BV000003166 816 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020668329&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parkinson, John B. Farnell, Damian J. J. An introduction to quantum spin systems Lecture notes in physics Quantenspinsystem (DE-588)4609091-5 gnd |
| subject_GND | (DE-588)4609091-5 |
| title | An introduction to quantum spin systems |
| title_auth | An introduction to quantum spin systems |
| title_exact_search | An introduction to quantum spin systems |
| title_full | An introduction to quantum spin systems John B. Parkinson, Damian J.J. Farnell |
| title_fullStr | An introduction to quantum spin systems John B. Parkinson, Damian J.J. Farnell |
| title_full_unstemmed | An introduction to quantum spin systems John B. Parkinson, Damian J.J. Farnell |
| title_short | An introduction to quantum spin systems |
| title_sort | an introduction to quantum spin systems |
| topic | Quantenspinsystem (DE-588)4609091-5 gnd |
| topic_facet | Quantenspinsystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020668329&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT parkinsonjohnb anintroductiontoquantumspinsystems AT farnelldamianjj anintroductiontoquantumspinsystems |