Regensburg 2016 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 73: Low-Dimensional Systems: Topological Order

TT 73.3: Vortrag

Donnerstag, 10. März 2016, 15:30–15:45, H19

Projective construction of the Zk Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry — •Cecile Repellin^1,2, Titus Neupert³, B. Andrei Bernevig⁴, and Nicolas Regnault^2,4 — ¹Max-Planck-Institut fur Physik complexer Systeme, Dresden, Germany — ²Laboratoire Pierre Aigrain, Ecole Normale Superieure, Paris, France — ³Princeton Center for Theoretical Science, Princeton, USA — ⁴Princeton University, Princeton, USA

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the Zk Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of Zk ground states on the torus. We develop an alternative projective construction of Zk Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.