Entanglement in resonating valence bond states: ladder versus isotropic lattices

We study the behavior of bipartite, as well as genuine multipartite, entanglement of a resonating valence bond state on a ladder. Although there is negligible bipartite entanglement (BE) present in the rails, as is the case for isotropic lattices in two and higher dimensions, we show that the system possesses significant amounts of BE in the steps of the ladder. However, we find that the genuine multipartite entanglement in the system is substantially low. Therefore, both the properties of bipartite as well as multipartite entanglement in the ladder are contrary to the behavior of entanglement in isotropic lattices, indicating that the geometry of the lattice can play a significant role in quantum information processing tasks. Our results also indicate that numerical and analytical investigations obtained on ladders cannot infer the same on two-dimensional lattices.