  Topological phases are unique states of matter incorporating long-range
quantum entanglement, hosting exotic excitations with fractional quantum
statistics. We report a practical method to identify topological phases in
arbitrary realistic models by accurately calculating the Topological
Entanglement Entropy (TEE) using the Density Matrix Renormalization Group
(DMRG). We argue that the DMRG algorithm naturally produces a minimally
entangled state, from amongst the quasi-degenerate ground states in a
topological phase. This proposal both explains the success of this method, and
the absence of ground state degeneracy found in prior DMRG sightings of
topological phases. We demonstrate the effectiveness of the calculational
procedure by obtaining the TEE for several microscopic models, with an accuracy
of order $10^{-3}$ when the circumference of the cylinder is around ten times
the correlation length. As an example, we definitively show the ground state of
the quantum $S=1/2$ antiferromagnet on the kagom\'e lattice is a topological
spin liquid, and strongly constrain the full identification of this phase of
matter.
