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Mercredi 25/05/2007 - 10H30 - Attention, jour et horaire inhabituels !

Valence bond worm and projector algorithms

Kevin Beach (Wurzburg Univ.)

par Webmaster - 25 avril 2007

In addition to states with ordered local moments, quantum magnets can support a variety of paramagnetic ground states that have no classical analogue. A natural description for these states is in terms of valence bonds (singlet pairs), which can exhibit liquid ("resonating") or crystalline behaviour.

The enormous overcompleteness of the valence bond basis makes it inappropriate for use with conventional algorithms that depend on orthonormality. Nonetheless, it is possible to exploit the overcompleteness by organizing a computation around the fact that overlaps of valence bond states are always nonzero and can be represented by a set of closed loops.

Using a recently developed valence bond projector algorithm, it is particularly easy to simulate Heisenberg-type models with additional SU(2)-invariant four- and higher-spin interactions that compete with antiferromagnetic order. In two- and three-dimensions, such interactions can be shown to drive the system into a bond-ordered state. Finally, I will discuss the prospects for simulating models with explicitly frustrating interactions.