1211.3733 (Michael P. Zaletel et al.)

Topological characterization of fractional quantum Hall ground states
from microscopic Hamiltonians    [PDF]

Michael P. Zaletel, Roger S. K. Mong, Frank Pollmann

We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. For finding the ground state, we employ the infinite density matrix renormalization group (iDMRG) method which is based on the matrix-product state (MPS) representation of FQH states on an infinite cylinder. From the MPS representation, we compute the topological entanglement entropies and the quasiparticle charges. Using pairs of degenerate groundstates as boundary conditions introduces localized quasiparticles of a chosen topological charge. 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 using data contained entirely in the entanglement spectrum.

View original: http://arxiv.org/abs/1211.3733