An Introduction to Quantum Spin Systems (Lecture Notes in Physics, 816)

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An Introduction to Quantum Spin Systems (Lecture Notes in Physics, 816)

Written by John B. Parkinson
4.85 52,516 ratings
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About this ebook:
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. Ofcoursetherearemanycasesinwhichwecan ndnoexactsolutionandinthese casestheycanbeusedasatestinggroundforapproximatemethodsofmodern-day quantummechanics. Thesequantumsystemsthusprovideagreatvarietyofint- estinganddif cultchallengestothemathematicianorphysicalscientist. Thisbookwaspromptedbyaseriesoftalksgivenbyoneoftheauthors(JBP)at asummerschoolinJyvaskyla, Finland. Thesetalksprovidedadetailedviewofhow onegoesaboutsolvingthebasicproblemsinvolvedintreatingandunderstanding spinssystemsatzerotemperature. Itwasthislevelofdetail, missingfromothertexts inthearea, thatpromptedtheotherauthor(DJJF)tosuggestthattheselecturesbe broughttogetherwithsupplementarymaterialinordertoprovideadetailedguide 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. . . . . . . . . . . . . . . . . . . . . . . . .

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Published August 28, 2010
ISBN 10057598
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John B. Parkinson
About the Author
John B. Parkinson

John B. Parkinson writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. John B. Parkinson lives with their spouse and a very vocal rescue cat.

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Jacob Wilson
Jacob Wilson March 27, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Rebecca Adams October 14, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Donald Green
Donald Green March 18, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Carol Mitchell
Carol Mitchell August 11, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Charles Gonzalez
Charles Gonzalez April 12, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Sarah Turner
Sarah Turner October 09, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Thomas Diaz
Thomas Diaz October 22, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Richard Evans September 21, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Brian Torres
Brian Torres December 11, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Anthony Wilson
Anthony Wilson December 25, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Amanda Young
Amanda Young March 06, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
William Moore
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An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
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An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
Michelle Allen
Michelle Allen March 27, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Joshua Lopez
Joshua Lopez September 04, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Anthony Clark
Anthony Clark January 27, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Jessica Johnson
Jessica Johnson October 15, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Stephanie Gomez
Stephanie Gomez November 09, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
David Williams
David Williams December 15, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Sandra Mitchell
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Kevin Rodriguez
Kevin Rodriguez October 12, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Kimberly Martinez
Kimberly Martinez July 01, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Thomas Allen
Thomas Allen May 27, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Elizabeth Nelson
Elizabeth Nelson August 02, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Anthony Martinez
Anthony Martinez March 13, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
James Wright
James Wright September 29, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Susan Thompson
Susan Thompson February 24, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Margaret Edwards
Margaret Edwards March 15, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Mary Walker
Mary Walker October 04, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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