  We prove that the ground states of a local Hamiltonian satisfy an area law
and can be computed in polynomial time when the interaction graph is a tree
with discrete fractal dimension $\beta<2$. This condition is met for generic
trees in the plane and for established models of hyperbranched polymers in 3D.
This work is the first to prove an area law and exhibit a provably
polynomial-time classical algorithm for local Hamiltonian ground states beyond
the case of spin chains. Our algorithm outputs the ground state encoded as a
multi-scale tensor network on the META-tree, which we introduce as an analogue
of Vidal's MERA. Our results hold for polynomially degenerate and frustrated
ground states, matching the state of the art for local Hamiltonians on a line.
