  We introduce a novel tensor network structure augmenting the well-established
Tree Tensor Network representation of a quantum many-body wave function. The
new structure satisfies the area law in high dimensions remaining efficiently
manipulatable and scalable. We benchmark this novel approach against
paradigmatic two-dimensional spin models demonstrating unprecedented precision
and system sizes. Finally, we compute the ground state phase diagram of
two-dimensional lattice Rydberg atoms in optical tweezers observing non-trivial
phases and quantum phase transitions, providing realistic benchmarks for
current and future two-dimensional quantum simulations.
