Dresden 2003 – wissenschaftliches Programm

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MA: Magnetismus

MA 23: Bio-und molekularer Magnetismus

MA 23.9: Vortrag

Donnerstag, 27. März 2003, 12:15–12:30, HSZ/401

Exact energy bounds for n-partite spin systems — •Jürgen Schnack, Klaus Bärwinkel, and Heinz-Jürgen Schmidt — Universität Osnabrück, Fachbereich Physik, Barbarastr. 7, D-49069 Osnabrück, Germany

Rigorous results on spin systems like the Marshall-Peierls sign rule and the famous theorems of Lieb, Schultz, and Mattis have sharpened our understanding of magnetic phenomena. In addition such results can serve as a basis or source of inspiration for the development of approximate models. For example, the inequalities of Lieb and Berezin relating spectral properties of quantum systems to those of their classical counterparts provide a foundation for classical or semi-classical treatments of spin systems.

In this talk we will extend the body of rigorous results on spin systems by generalizing the notion of “bi-partitenessNo-dq. The introduction of the concept of n-partite spin systems enables us to derive new upper bounds for the minimal energies Emin in each subspace H(M) of total magnetic quantum number M for XXZ models and new lower bounds for the minimal energies in each subspace of total spin quantum number S for Heisenberg models. The bounds are derived for arbitrary single-spin quantum number s. The resulting bounds improve earlier findings especially for frustrated spin systems.

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