  We show how to numerically calculate several quantities that characterize
topological order starting from a microscopic fractional quantum Hall (FQH)
Hamiltonian. To find the set of degenerate ground states, we employ the
infinite density matrix renormalization group (iDMRG) method based on the
matrix-product state (MPS) representation of FQH states on an infinite
cylinder. To study localized quasiparticles of a chosen topological charge, we
use pairs of degenerate ground states as boundary conditions for the iDMRG. We
then show that the wave function obtained on the infinite cylinder geometry can
be adapted to a torus of arbitrary modular parameter, which allows us to
explicitly calculate the non-Abelian Berry connection associated with the
modular T-transformation. As a result, the quantum dimensions, topological
spins, quasiparticle charges, chiral central charge, and Hall viscosity of the
phase can be obtained using data contained entirely in the entanglement
spectrum of an infinite cylinder.
