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

Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians