**Taking the frustration out of quantum spin systems**

Geometric frustration a occurs in antiferromagnetic spin systems
on lattices with a topology where the energy of each interacting
pair of spins cannot be minimized individually. Examples are
triangular, Kagome and Pyrochlor lattices. The latter have tetrahedral
unit cells. A characteristic property of frustrated spin systems is
the large degeneracy of classical ground states. Little is known
exactly about these interesting physical systems. Even less is
known about the corresponding quantum spin systems. The only
knowledge about these complicated systems has so far been
based on elaborate numerical simulations. With the help of
sharp matrix inequalities and tricks of mathematical physics
that stem from early work on quantum field theory, it is, however,
possible to obtain interesting exact results about the ground
state and excitations of frustrated quantum spin systems.
The talk is based on joint work with Elliott Lieb. It includes a
brief introduction to quantum spins.

*Peter Schupp*

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