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- Fractional Quantum Hall States on an infinite cylinder: characterizing topological order and quasiparticle forces using infinite DMRG.

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PIRSA Number:

13020129

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.

©2012 Perimeter Institute for Theoretical Physics