An Introduction to Quantum Spin Systems

Erscheinungsjahr 2010
ISBN: 978-3-642-13289-6
Verlag: Springer

Buch, Englisch, Band 816, 154 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 540 g

Reihe: Lecture Notes in Physics

whichmightbeofuse,perhapstoagraduatestudentstartingworkinthisarea. Thebookisorganisedintochaptersthatdeal rstlywiththenatureofquantum mechanicalspinsandtheirinteractions. Thefollowingchaptersthengiveadetailed guidetothesolutionoftheHeisenbergandXYmodelsatzerotemperatureusing theBetheAnsatzandtheJordan-Wignertransformation,respectively. Approximate methodsarethenconsideredfromChap. 7onwards,dealingwithspin-wavet- oryandnumericalmethods(suchasexactdiagonalisationsandMonteCarlo). The coupledclustermethod(CCM),apowerfultechniquethathasonlyrecentlybeen vii viii Preface appliedtospinsystemsisdescribedinsomedetail. The nalchapterdescribesother work,someofitveryrecent,toshowsomeofthedirectionsinwhichstudyofthese systemshasdeveloped. Theaimofthetextistoprovideastraightforwardandpracticalaccountofall of the steps involved in applying many of the methods used for spins systems, especiallywherethisrelatestoexactsolutionsforin nitenumbersofspinsatzero temperature. Inthisway,wehopetoprovidethereaderwithinsightintothesubtle natureofquantumspinproblems. Manchester,UK JohnB. Parkinson January2010 DamianJ. J. Farnell Contents 1 Introduction. 1 References. 5 2 Spin Models. 7 2. 1 SpinAngularMomentum. 7 2. 2 CoupledSpins. 10 1 2. 3 TwoInteractingSpin- ’s. 11 2 2. 4 CommutatorsandQuantumNumbers. 14 2. 5 PhysicalPicture. 16 2. 6 In niteArraysofSpins. 16 1 2. 7 1DHeisenbergChainwith S = andNearest-Neighbour 2 Interaction. 18 References. 19 1 3 Quantum Treatment of the Spin- Chain. 21 2 3. 1 GeneralRemarks. 21 3. 2 AlignedState. 22 3. 3 SingleDeviationStates. 23 3. 4 TwoDeviationStates. 27 3. 4. 1 FormoftheStates. 33 3. 5 ThreeDeviationStates. 36 Z N 3. 5. 1 BetheAnsatzforS = ?3. 36 T 2 3. 6 StateswithanArbitraryNumberofDeviations. 37 Reference. 38 4 The Antiferromagnetic Ground State. 39 4. 1 TheFundamentalIntegralEquation. 39 4. 2 SolutionoftheFundamentalIntegralEquation. 43 4. 3 TheGroundStateEnergy. 45 References. 47 ix x Contents 5 Antiferromagnetic Spin Waves. 49 5. 1 TheBasicFormalism. 49 5. 2 MagneticFieldBehaviour.

Zielgruppe

Research

Autoren/Hrsg.

Parkinson, John B.

Farnell, Damian J. J.

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Spin Models.- Quantum Treatment of the Spin-½ Chain.- The Antiferromagnetic Ground State.- Antiferromagnetic Spin Waves.- The XY Model.- Spin-Wave Theory.- Numerical Finite-Size Calculations.- Other Approximate Methods.- The Coupled Cluster Method.- Quantum Magnetism.