Condensed Matter Seminars

The quantum Hall effect is an exotic phenomena found in nature. At fractional filling, these phases support fractional charge excitations with anyonic braiding statistics, which may be suitable for topological quantum computation. I will discuss the recent progress on studying these phases using matrix product states (MPSs) and the density-matrix-renormalization group (DMRG) technique. On one hand the MPS structure for quantum Hall reveals deep connection between quantum entanglement, conformal field theory, and topological field theory. Pragmatically, an understanding of the MPS structure allows us to perform efficient DMRG simulations for physical quantum Hall systems. There, the key advance is to reliably get the ground state wavefunction from a microscopic Hamiltonian, and to be able to identify the braiding statistics of the excitations solely from the ground state. Finally, I will also discuss various applications of these numerical methods.