Numerical Analysis of Quasiholes of the Moore-Read Wavefunction

Details Numerical Analysis of Quasiholes of the Moore-Read Wavefunction Numerical Analysis of Quasiholes of the Moore-Read Wavefunction

2009-01-22

arxiv.org/abs/0901.3502v2

Phys. Rev. Lett. 103, 076801 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.103.076801

We demonstrate numerically that non-Abelian quasihole excitations of the $\nu = 5/2$ fractional quantum Hall state have some of the key properties necessary to support quantum computation. We find that as the quasihole spacing is increased, the unitary transformation which describes winding two quasiholes around each other converges exponentially to its asymptotic limit and that the two orthogonal wavefunctions describing a system with four quasiholes become exponentially degenerate. We calculate the length scales for these two decays to be $\xi_{U} \approx 2.7 \ell_0$ and $\xi_{E} \approx 2.3 \ell_0$ respectively. Additionally we determine which fusion channel is lower in energy when two quasiholes are brought close together.

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