  Here we show how the Minimally Entangled States (MES) of a 2d system with
topological order can be identified using the geometric measure of
entanglement. We show this by minimizing this measure for the doubled semion,
doubled Fibonacci and toric code models on a torus with non-trivial topological
partitions. Our calculations are done either quasi-exactly for small system
sizes, or using the tensor network approach in [R. Orus, T.-C. Wei, O.
Buerschaper, A. Garcia-Saez, arXiv:1406.0585] for large sizes. As a byproduct
of our methods, we see that the minimisation of the geometric entanglement can
also determine the number of Abelian quasiparticle excitations in a given
model. The results in this paper provide a very efficient and accurate way of
extracting the full topological information of a 2d quantum lattice model from
the multipartite entanglement structure of its ground states.
