Simulating quantum systems on classical computers with matrix product states [Elektronische Ressource] / Adrian Kleine

Simulating Quantum Systems onClassical Computers withMatrix Product StatesVon der Fakult¨at fu¨r Mathematik, Informatik undNaturwissenschaften der RWTH Aachen Universityzur Erlangung des akademischen Grades eines Doktorsder Naturwissenschaften genehmigte Dissertationvorgelegt vonDiplom - PhysikerAdrian Kleineaus AachenBerichter: Universit¨atsprofessor Dr. Ulrich Schollw¨ockUniversit¨atsprofessorin Dr. Sabine AndergassenTag der mu¨ndlichen Pru¨fung: 8. November 2010Diese Dissertation ist auf den Internetseiten derHochschulbibliothek online verfu¨gbarAbstractInthisthesis,thenumericalsimulationofstrongly-interactingmany-bodyquantum-mechanicalsystems using matrix product states (MPS) is considered. Compared to classical systems,quantum many-body systems possess an exponentially enlarged number of degrees of free-dom, significantly complicating a simulation on a classical computer.Matrix-Product-States are a novel representation of arbitrary quantum many-body states.Using quantum information theory, it is possible to show that Matrix-Product-States pro-vide a polynomial-sized representation of one-dimensional quantum systems, thus allowingan efficient simulation of one-dimensional quantum system on classical computers. Matrix-Product-States form the conceptual framework of the density-matrix renormalization group(DMRG).Baseduponthisconnection, deeperunderstandingofthedensitymatrixrenormal-ization group can be obtained.