Regensburg 2004 – wissenschaftliches Programm

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TT: Tiefe Temperaturen

TT 26: Korrelierte Elektronen: Theorie II

TT 26.4: Vortrag

Donnerstag, 11. März 2004, 10:15–10:30, H18

Effective Models by Self–Similar Continuous Unitary Transformations: the Hubbard Model at Strong Coupling — •Alexander Reischl, Erwin Müller-Hartmann, and Götz Silvester Uhrig — Institut für theoretische Physik, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany

An effective model conserving the number of double occupancies is derived for the half–filled Hubbard model at strong coupling.

The mapping to the effective model is performed by a self–similar continuous unitary transformation (CUT). The sectors of different double occupancy are decoupled. Therefore the effective model is a generalized t–J–model. A truncation scheme that selects operators according to their locality is used to close the flow equations.

The convergence and accuracy of the method are discussed in the light of the developing itinerant character of the system for increasing bandwidth. The apparent energy–gap for a single hole or a double occupancy is calculated within the effective model.

Our main result is that the mapping of the Hubbard–Model to the t–J–model is possible and very robust as long as the apparent gap is positive. In this regime relatively small clusters suffice to determine the parameters of the effective model reliably. Besides correlated hopping and interaction of charges the most prominent interactions are the two–spin nearest neighbor exchange and the four–spin ring–exchange.