Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices

Understand

We show for several two-dimensional lattices that the nearest neighbor valence bond states are linearly independent.

• To do so, we utilize and generalize a method that was recently introduced and applied to the kagome lattice by one of the authors.
• This method relies on the choice of an appropriate cell for the respective lattice, for which a certain local linear independence property can be demonstrated.
• Whenever this is achieved, linear independence follows for arbitrarily large lattices that can be covered by such cells, for {\em both} open and periodic boundary conditions.