  Frustration and quantum entanglement are two exotic quantum properties in
quantum many-body systems. However, despite several efforts, an exact relation
between them remains elusive. In this work, we explore the relationship between
frustration and quantum entanglement in a physical model describing strongly
correlated ultracold bosonic atoms in optical lattices. In particular, we
consider the one-dimensional Bose-Hubbard model comprising both
nearest-neighbor ($t_{1}$) and frustrated next-nearest neighbor ($t_{2}$)
hoppings and examine how the interplay of onsite interaction ($U$) and hoppings
results in different quantum correlations dominating in the ground state of the
system. We then analyze the behavior of quantum entanglement in the model. In
particular, we compute genuine multipartite entanglement as quantified through
the generalized geometric measure and make a comparative study with bipartite
entanglement and other relevant order parameters. We observe that genuine
multipartite entanglement has a very rich behavior throughout the considered
parameter regime and frustration does not necessarily favor generating a high
amount of it. Moreover, we show that in the region with strong quantum
fluctuations, the particles remain highly delocalized in all momentum modes and
share a very low amount of both bipartite and multipartite entanglement. Our
work illustrates the necessity to give separate attention to dominating
ordering behavior and quantum entanglement in the ground state of strongly
correlated systems.
