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New Computational Techniques for Strongly Correlated Electron Systems

New Computational Techniques for Strongly Correlated Electron Systems

          
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About the Book

Die Arbeit stellt in einem ersten, "technischen" Teil wichtigeVerfahren zur numerischenSimulation hoch korrelierter Elektronensysteme vor, beschreibteigene Beitrage zur Weiterentwicklung der Verfahrenund liefert exemplarische Anwendungen auf moderne Forschungsprobleme. In einem zweiten, "physikalischen" Teil werden neuenummerische Ergebnisse zur SO(5)-Theorie derHochtemperatur-Supraleitung dargestellt. Der erste Teil der Arbeit zeigt zunachst, wie fur Fermionensystemeeffektive Modelle konstruiert werden konnen, in denen die niederenergetischePhysik durch bosonische Quasiteilchenausgedruckt wird. Insbesondere wird ein Vier-Bosonen-Modellfur zweidimensionale Elektronensysteme hergeleitet, die sich auf mikroskopischer Ebene durch das Heisenberg- oder T-J-Modell beschreiben lassen. Das wichtigste reale Anwendungsgebiet dieser Modelle sind die Kuprat-Supraleiter. Anschliessend wird die Technik der Exakten Diagonalisierung (ED) vorgestellt, wobei die effiziente Implementierung auf modernen Hochstleistungsrechnern breiten Raum einnimmt.Eine Studie der Metall-Isolator-Ubergange imHubbard-Modell bei Halbfullung - einem Modell fur die undotierten Ausgangsmaterialien derKuprat-Supraleiter - enthullt als eine exemplarische Anwendung der EDein vielgestaltigesPhasendiagramm mit zwei verschiedenen metallischen und zwei isolierendenPhasen (vom Typ Mott-Heisenberg-Isolator und Mott-Hubbard-Isolator).In einer zweiten Anwendung werden experimentellgemessene Rontgen-Zirkulardichroismus-Spektren destechnologisch interessanten magnetischen Halbmetalls CrO,2 im Computerexperiment reproduziert, so dass die elementarenWechselwirkungsprozesse in dem Material quantitativ bestimmt werden konnen. Exemplarisch fur die Quanten-Monte-Carlo-Simulationstechniken wird die stochastische Reihenentwicklung (SSE) beschrieben, wobei eine neue Methode zur effizienten Messung beliebiger Greenscher Funktionen entwickelt wird. Deren exzellentes Skalierungsverhalten wird in drei Anwendungen belegt, welche die Zerstorung der suprafluiden und langreichweitigen Ordnung in zweidimensionalen Vielteilchensystemen, die Quanten-Phasenubergange im Hardcore-Bosonenmodell undschliesslich die Spin-1/2-Heisenbergleiter - ein Modellsystemfur Zinkverunreinigungen in Kuprat-Supraleitern - untersuchen. Der "technische" Teil endet mit Uberlegungenzum Computereinsatz bei muhsamen algebraischen Termumformungen, wie sie bei der analytischen Behandlung von Vielteilchensystemen entstehen. Das entstandene Mathematica-Programm wird fur eineUntersuchung des Hubbard-Modells verwendet, welche die sogenannte Hubbard-I-Naherung und deren Versagen bei Halbfullung und starker Wechselwirkung studiert. Der zweite grosse Teil der Arbeit ist einer ausfuhrlichen nummerischen Analyse des projiziertenSO(5)-symmetrischen Modells der Hochtemperatur-Supraleitung gewidmet. Dieses Modell bildet die niederenergetische Physik der CuO2 Ebenenin den Kuprat-Supraleitern auf ein System aus vier bosonischenQuasiteilchen-Typen ab: drei Triplett-Anregungen und eine Lochpaar-Anregung. Nummerische Simulationsergebnisse an zwei- und dreidimensionalenGittergeometrien zeigen, dass das pSO(5)-Modell viele Eigenschaften derHochtemperatursupraleiter in halbquantitativer oder sogar quantitativerWeise richtig widergibt, insbesondere die Existenz und die Form einer antiferromagnetischen und einer supraleitenden Phase, die Dotierungsabhangigkeit des chemischen Potenzials und den Resonanzpeak in Neutronenstreuexperimentenim unterdotierten Bereich.


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Product Details
  • ISBN-13: 9783832502287
  • Publisher: Logos Verlag Berlin
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 0 mm
  • Width: 169 mm
  • ISBN-10: 3832502289
  • Publisher Date: 30 May 2002
  • Height: 240 mm
  • No of Pages: 222
  • Series Title: English
  • Weight: 700 gr

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