Simulating quantum systems in the valence bond basis

Kevin Beach Boston University

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.