Gifting Made Simple
Give the Gift of ChoiceClick below to purchase a Bramalea City Centre eGift Card that can be used at participating retailers at Bramalea City Centre.Purchase HereHome
An Introduction to Quantum Spin Systems
Coles
Loading Inventory...
An Introduction to Quantum Spin Systems in Brampton, ON
Current price: $51.59
Original price: $64.49
Coles
An Introduction to Quantum Spin Systems in Brampton, ON
Current price: $51.59
Original price: $64.49
Loading Inventory...
Size: Kobo eBook
*Product information and pricing may vary - to confirm current pricing, availability, shipping, and return information please contact Coles. In the event of a pricing discrepancy, the retailer's price will apply.
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
You May Also Like
Find at Bramalea City Centre in Brampton, ON
Visit at Bramalea City Centre in Brampton, ON