Abstract:
In a system of quantum spins, the set of all possible valence bond
tilings spans the singlet ground state. Until recently, this basis was
used primarily in theoretical work---e.g., to construct RVB-like trial
wavefunctions---but rarely for numerical computation. The enormous
overcompleteness of the basis makes it inappropriate for use with
conventional algorithms that depend on orthonormality. It is now
understood how to implement a numerical projection scheme that takes
advantage of the overcompleteness [cond-mat/0509558]. I will discuss
the prospects for a highly-efficient transposition-list implementation
and for extending the valence bond basis to include charge degrees of
freedom.