پديد آورنده :
قرباني، الهه
عنوان :
بررسي تحول زماني triplon در ملكول بنزن و محاسبه ي حالت پايه ي وردشتي RVB پلي اسين ها به روش شبيه سازي مونت كارلوي كوانتومي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده فيزيك
صفحه شمار :
[ده]،98ص.: مصور،جدول،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
اكبر جعفري
استاد مشاور :
فرهاد شهبازي
تاريخ نمايه سازي :
8/3/90
استاد مدعو :
پيمان صاحب سرا
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Dynamics of triplons in benzene and variational Monte Carlo study of RVB ground state in polyacene Elaheh Ghorbani el ghorbani@gmail com March 12 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language PersianS A Jafari akbar jafari@gmail comAbstractIn this thesis we investigate the resonating valence bond RVB description of aromatic compounds We start by introducing the Heisenberg Hamiltonian and describe its ground and excited states inthe valence bond VB basis Excited states are constructed from the very same basis by turningone of the singlets into triplet Such excited states are called triplons We derive the calculus ofsuch wave functions by calculating the matrix elements of the Hamiltonian and the unit operatorbetween such states These results are general and are valid for arbitrary planar lattice and arbitrarynumber of triplons We use these rules to construct exact ground and excited states of the benzenemolecule We con rm that as pointed out by Kekule the short VB con gurations in benzene aredominant both in ground and excited states This is quanti ed in terms of a very small ration ofthe con gurations involving longer singlets triplets Next we study the dynamics of one triplon inthe benzene molecule employing the Green s function method In agreement with the qualitativepicture of the ground and one triplon excited states the transition from short bond con gurationsto those with longer bonds are not likely to occur Our analytic results for benzene molecule havebeen con rmed by numeric methods Adding up Resonating valence bond RVB states are suitablecandidates for the ground state of the Heisenberg model on various two dimensional lattices Whena singlet valence bond is broken to produce state the resulting excitation is called a triplon In thisthesis we obtain formulas for the overlap and also matrix elements of operator between states witharbitrary number of triplons our resultes are valid for any 2D lattice Then considering Resonating Valence Bond RVB as a Ground state of the Heisenberg model for the benzene molecule we in vestigate triplet excited states Eigen values are calculated both analytically and numerically Wehave expand the ground and rst excited states in terms of valence bond VB con guration sincethe momentum of rst excited state is k 0 We investigate of Green function in the vector of VBbases In other word we expand the ground and rst excited states in terms of valence bond VB con guration For VB con gurations with largest weight we investigate the time evolution of anadded triplon In the second part of the thesis we consider a linear chain of such molecules theso called polyacene We implement the rules obtained in the rst part on the computer for largersystems to stochastically optimize a wave function constructed from the VB con gurations for theground state of polyacene The computer code is benchmarked against existing literature for squareand honeycomb lattice where we nd some residual Neel order In the case of polyacene we ndthat the ground state is a gapped spin liquid characterized with short range correlations and no longrange Neel order Acenes or polyacenes is a class of organic compounds and polycyclic aromatichydrocarbons made up of linearly fused benzene rings The larger representatives have potentialinterest in optoelectronic applications and are actively researched in chemistry and electrical engi neering Key Words RVB VB Triplon Benzene molecule Polyacine
استاد راهنما :
اكبر جعفري
استاد مشاور :
فرهاد شهبازي
