Regensburg 2013 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 3: Correlated Electrons: Low-Dimensional Systems - Models 1
TT 3.12: Vortrag
Montag, 11. März 2013, 12:30–12:45, H9
Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians — •Frank Pollmann1, Michael P. Zaletel2, and Roger S. K. Mong3 — 1Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany — 2Department of Physics, University of California, Berkeley, California 94720, USA — 3Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
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. We furthermore 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. As a result, the topological spins, central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum.