Geometry versus Entanglement in Resonating Valence Bond Liquids

TL;DR

This paper explores how the geometry of a lattice influences the distribution of bipartite and multipartite entanglement in resonating valence bond states, revealing significant bipartite entanglement in ladder structures but negligible multipartite entanglement.

Contribution

It demonstrates the impact of lattice geometry on entanglement properties, contrasting ladder and higher-dimensional lattice behaviors in RVB states.

Findings

Significant bipartite entanglement in ladder steps

Negligible bipartite entanglement in rails

Geometry affects quantum information potential

Abstract

We investigate the behavior of bipartite as well as genuine multipartite entanglement of a resonating valence bond state on a ladder. We show that the system possesses significant amounts of bipartite entanglement in the steps of the ladder while no substantial bipartite entanglement is present in the rails. Genuine multipartite entanglement present in the system is negligible. The results are in stark contrast with the entanglement properties of the same state on isotropic lattices in two and higher dimensions, indicating that the geometry of the lattice can have important implications on the quality of quantum information and other tasks that can be performed by using multiparty states on that lattice.