Tensor networks provide descriptions of strongly correlated quantum
systems based on an underlying entanglement structure given by a graph
of entangled states along the edges that identify the indices of the
local tensors to be contracted. Considering a more general setting,
where entangled states on edges are replaced by multipartite entangled
states on faces, allows us to employ the geometric properties of
multipartite entanglement in order to obtain representations in terms of
superpositions of tensor network states with smaller effective
dimension, leading to computational savings.
Simulating strongly correlated quantum systems with tree tensor networks