Holdings: An introduction to quantum spin systems

An introduction to quantum spin systems:

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Bibliographic Details
Main Authors:	Parkinson, John B. (Author), Farnell, Damian J. J. (Author)
Format:	Book
Language:	English
Published:	Heidelberg ; Dordrecht ; London ; New York Springer [2010]
Series:	Lecture notes in physics 816
Subjects:	Quantenspinsystem
Online Access:	Inhaltsverzeichnis
Physical Description:	xi, 154 Seiten Diagramme
ISBN:	9783642132896

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MARC


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Record in the Search Index

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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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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
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