The density matrix renormalization group (DMRG), which
has proved so successful in one dimension, has been making the push into higher
dimensions, with the fractional quantum Hall (FQH) effect an important target.
I'll briefly explain how the infinite DMRG algorithm can be adapted to find the
degenerate ground states of a microscopic FQH Hamiltonian on an infinitely long
cylinder, then focus on two applications. To characterize the topological order
of the phase, I'll show that the bipartite entanglement spectrum of the ground
state is sufficient to determine the quasiparticle charges, topological spins,
quantum dimensions, chiral central charge, and Hall viscosity of the phase.
Then I will show how to introduce localized quasiparticles of fixed topological
charge. By pinning a pair of quasiparticles and dragging them into contact, we
can directly measure the force curve of their interaction.