Hubbard model with geometrical frustration [Elektronische Ressource] / vorgelegt von Hunpyo Lee

Hubbard model with geometrical frustrationDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakult atderRheinischen Friedrich-Wilhelms-Universit at Bonnvorgelegt vonHunpyo LeeausKangnung, South KoreaBonn, October 2009Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult atder Rheinischen Friedrich-Wilhelms-Universit at Bonn.1. Gutachter: Prof. Dr. H. Monien2.hter: Prof. Dr. R. FlumeTag der Promotion: 8.10.2009Erscheinungsjahr: 20103AbstractAt rst we present the details of the dual fermion (DF), the cluster extension ofdynamical mean eld theory (CDMFT) and continuous-time quantum Monte Carlo(CT QMC) methods. Using a panoply of these methods we explore the Hubbardmodel on the triangular and hyperkagome lattice. We nd a rst-order transitionand continuous transition on the triangular and hyper-kagome lattice, respectively.Moreover, we nd the reentrant behavior due to competition between the magneticcorrelation and itinerancy of electrons by source of geometrical frustration on bothlattices.4Contents1 Approximations and impurity solvers 71.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.1 Dynamical mean eld theory . . . . . . . . . . . . . . . . . . . 91.2.2 Cluster-extension of the DMFT method . . . . . . . . . . . . 111.2.3 Dual fermion method . . . . . . . . .