Dresden 2009 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 42: Correlated Electrons: Low-dimensional Systems - Models 2

TT 42.6: Talk

Thursday, March 26, 2009, 15:15–15:30, HSZ 301

Momentum classification of SU(n) spin chains with arbitray representations using Young Tableaux — •Burkhard Scharfenberger and Martin Greiter — Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe

Recently, Schuricht and one of us [Phys. Rev. Lett. 98, 237202(2007)] established a correspondence between the Young tableaux classifying the total spin representations of N SU(n) spins and eigenstates of the SU(n) Haldane–Shastry model for a chain of N sites. As a side product, this correspondence provides a direct link between total spin and total linear momentum content of the representations for spin chains with individual spins transforming under fundamental representations of SU(n) in general, i.e. the formalism can be used to read of directly how many of the total spin singlets have total momentum zero and so on. Here, we introduce a general tableau formalism for combining N spins transforming under an arbitrary representation of SU(n) into representations of total spin, with which we establish a set of rules how to obtain the linear momentum content of these representations for spin chains with N sites. The perspective goal of these studies is to set up a formalism to perform exact diagonalization studies of spin rotationally invariant models of spin chains (and eventually arbitrary lattices) in Hilbert space subspaces with both well defined total momentum (quantum numbers under lattice symmetries) and total spin.