7032

6574

كارشناسي ارشد

ماده چگال

اصفهان: دانشگاه صنعتي اصفهان، دانشكده فيزيك

1390

ده، 77ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

فرهاد شهبازي

كيوان آقابابائي ساماني

11/7/91

فرهاد فضيله، علي اكبر بابائي بروجني

1396/09/18

كتابنامه

فيزيك

فيزيك

ID6574

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

The Usage of Continuous Unitary Transformation to Produce Effective Hamiltonian for Hubbard Model Sajjad Salimy Nanekarani s salimynanekarani@ph iut ac ir March 7 2012 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Laguage Farsi Mail shahbazi@cc iut ac ir Dr Farhad Shahbazi AbstractSince the Quantum Mechanics invented people always look for procedure to explain many particle problems Ingeneral a procedure for solve Quantum Mechanics problem lead to find eigenstates that is equivalent to block diagonalization of Hamiltonian But in many particle systems finding of this eigenstates when interactionbetween particles of system is not negligible is really hard work and mostly there is no solution for the problem To overcome this difficulty one of the simplest procedures is simplification of the picture of the Hamiltonian For do this sometimes change of the basis is useful Hence one must look for such transformation whichincreases the zeros of the Hamiltonian matrix although doesn t make diagonal matrix In this thesis theprocedure we chose was Continuous Unitary Transformation This method at first was invented by F J Wegner In this method operation that is done is produce generator for transformation which is function of continuesparameter Using of this generator leads flow equation that is set of first order differential equations Variation ofcontinuous parameter is how to change original matrix to block diagonal matrix To produce generator it can behelpful to use quasi particle concept Here particles are excitations of the system Generator which is intendedshould be independent of the shape of Hamiltonian The generator that Wegener used for its own purposes wascommutator of diagonal part of Hamiltonian with the total Hamiltonian In this thesis chosen generator iscommutator of number operator of quasi particle and total Hamiltonian When continuous parameter is infinitethen effective Hamiltonian will be produced The effect of resulting Hamiltonian in quasi particle just replacesthe quasi particle in effective lattice because of conserving the number of particles Here we are going to findeffective Hamiltonian for Hubbard Hamiltonian This Hamiltonian is divided to two parts kinetic energy andCoulomb interaction energy When ratio of kinetic energy to Coulomb energy is small but is not negligible so inthis regime pertubativly expanding the Hamiltonian will be useful and expanding parameter is ratio of kineticenergy to Coulomb energy with Pertubative Continuous Unitary Transformation effective Hamiltonian will beproduced In general each site of system can take all of four states from completely occupied to completelyempty but here we considered just half field states because these states are in the lowest energy states Hereexistence of doubly occupied state shows that there is quasi particle and one doubly occupied state is equivalentto one quasi particle In this procedure usage of Hubbard operators produce spin Hamiltonian Spin Hamiltonianincludes coupled terms interactions that represent Heisenberg interactions for different neighbors and some newkind of interactions so called ring exchange interactions Expressing Hamiltonian in spin representation showsthat local Hilbert space decrease from four states to two different states Key words Quantum Mechanics Many body Physics Continuous Unitary Transformation Quasi particle PerturbativeExpansion Hubbard Model Heisenberg Interactons and Ring Exchange

فرهاد شهبازي

كيوان آقابابائي ساماني

فرهاد فضيله، علي اكبر بابائي بروجني