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The topic of lattice quantum spin systems is a fascinating and by now well established branch of theoretical physics. Based on a set of lectures, this book has a level of detail missing from others, and guides the reader through the fundamentals of the field.
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The topic of lattice quantum spin systems is a fascinating and by nowwell-established branch of theoretical physics. However, many important questions remain to be answered. Their intrinsically quantum mechanical nature and the large (usually effectively infinite) number of spins in macroscopic materials often leads to unexpected or counter-intuitive results and insights. Spin systems are not only the basic models for a whole host of magnetic materials but they are also important as prototypical models of quantum systems. Low dimensional systems (as treated in this primer), in 2D and especially 1D, have been particularly fruitful because their simplicity has enabled exact solutions to be determined in many cases. These exact solutions contain many highly nontrivial features. This book was inspired by a set of lectures on quantum spin systems and it is set at a level of practical detail that is missing in other textbooks in the area. It will guide the reader through the foundations of the field. In particular, the solutions of the Heisenberg and XY models at zero temperature using the Bethe Ansatz and the Jordan-Wigner transformation are covered in some detail. The use of approximate methods, both theoretical and numerical, to tackle more advanced topics is considered. The final chapter describes some very recent applications of approximate methods in order to show some of the directions in which the study of these systems is currently developing.
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An Introduction to Quantum Spin Systems (Lecture Notes in Physics, 816)
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Springer (edition 2010), 2010
ISBN 10: 3642132898
ISBN 13: 9783642132896
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Paperback. Zustand: Very Good. 2010. It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting. Bestandsnummer des Verkäufers 3642132898-8-1
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Parkinson:An Introduction to Quantum Sp (eng)
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Introduction to Quantum Spin Systems
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An Introduction to Quantum Spin Systems (Paperback)
ISBN 10: 3642132898
ISBN 13: 9783642132896
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Paperback. Zustand: new. Paperback. The topic of lattice quantum spin systems (or 'spin systems' for short) is a f- cinating branch of theoretical physics and one of great pedigree, although many importantquestionsstillremaintobeanswered. The'spins'areatomic-sizedm- netsthatarelocalisedtopointsonalatticeandtheyinteractviathelawsofquantum mechanics. Thisintrinsicquantummechanicalnatureandthelarge(usuallyeff- tivelyin nite)numberofspinsleadstostrikingresultswhichcanbequitedifferent fromclassicalresultsandareoftenunexpectedandindeedcounter-intuitive. Spinsystemsconstitutethebasicmodelsofquantummagneticinsulatorsandso arerelevanttoawholehostofmagneticmaterials. Furthermore,theyareimportant asprototypicalmodelsofquantumsystemsbecausetheyareconceptuallysimple and yet stilldemonstrate surprisingly rich physics. Low dimensional systems, in 2Dandespecially1D,havebeenparticularlyfruitfulbecausetheirsimplicityhas enabledexactsolutionstobefoundwhichstillcontainmanyhighlynon-trivialf - tures. Spinsystemsoftendemonstratephasetransitionsandsowecanusethemto studytheinterplayofthermalandquantum uctuationsindrivingsuchtransitions.Ofcoursetherearemanycasesinwhichweca n ndnoexactsolutionandinthese casestheycanbeusedasatestinggroundforapproximatemethodsofmodern-day quantummechanics. Thesequantumsystemsthusprovideagreatvarietyofint- estinganddif cultchallengestothemathematicianorphysicalscientist. Thisbookwaspromptedbyaseriesoftalksgivenbyoneoftheauthors(JBP)at asummerschoolinJyvaskyla,Finland. Thesetalksprovidedadetailedviewofhow onegoesaboutsolvingthebasicproblemsinvolvedintreatingandunderstanding spinssystemsatzerotemperature. Itwasthislevelofdetail,missingfromothertexts inthearea,thatpromptedtheotherauthor(DJJF)tosuggestthattheselecturesbe broughttogetherwithsupplementarymaterialinordertoprovideadetailedguide whichmightbeofuse,perhapstoagraduatestudentstartingworkinthisare a. 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- 'areatomic-sizedm- netsthatarelocalisedtopointsonalatticeandtheyinteractviathelawsofquantum mechanics. Thisintrinsicquantummechanicalnatureandthelarge(usuallyeff- tivelyin nite)numberofspinsleadstostrikingresultswhichcanbequitedifferent fromclassicalresultsandareoftenunexpectedandindeedcounter-intuitive. Spinsystemsconstitutethebasicmodelsofquantummagneticinsulatorsandso arerelevanttoawholehostofmagneticmaterials.Furthermore,theyarei mportant asprototypicalmodelsofquantumsystemsbecausetheyareconceptuallysimple and yet stilldemonstrate surprisingly rich physics. Low dimensional systems, in 2Dandespecially1D,havebeenparticularlyfruitfulbecausetheirsimplicityhas enabledexactsolutionstobefoundwhichstillcontainmanyhighlynon-trivialf- tures. Spinsystemsoftendemonstratephasetransitionsandsowecanusethemto studytheinterplayofthermalandquantum uctu Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9783642132896
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