Parkinson J.B. An introduction to quantum spin systems (Berlin; Heidelberg; New York, 2010). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаParkinson J.B. An introduction to quantum spin systems / J.B.Parkinson, D.J.J.Farnell. - Berlin; Heidelberg; New York: Springer-Verlag, 2010. - xi, 154 p. - (Lecture notes in physics; 816). - Incl. bibl. ref. - Ind.: p.153-154. - ISBN 978-3-642-13289-6
 

Оглавление / 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-1/2's ............................. 11
   2.4  Commutators and Quantum Numbers ........................ 14
   2.5  Physical Picture ....................................... 16
   2.6  Infinite Arrays of Spins ............................... 16
   2.7  ID Heisenberg Chain with S = 1/2 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  SZ/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
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
        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 J1-J2 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 J1-J2 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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