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arXiv · 1401.4673

Construction of the edge states in fractional quantum Hall systems by Jack polynomial

Ki Hoon Lee·Zi-Xiang Hu·Xin Wan
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Abstract

We study the edge-mode excitations of a fractional quantum Hall droplet by expressing the edge state wavefunctions as linear combinations of Jack polynomials with a negative parameter. We show that the exact diagonalization within subspace of Jack polynomials can be used to generate the chiral edge-mode excitation spectrum in the Laughlin phase and the Moore-Read phase with realistic Coulomb interaction. The truncation technique for the edge excitations simplifies the procedure to extract reliably the edge-mode velocities, which avoids the otherwise complicated analysis of the full spectrum that contains both edge and bulk excitations. Generalization to the Read-Rezayi state is also discussed.

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Ki Hoon Lee, Zi-Xiang Hu, Xin Wan. 2014-01-19. Construction of the edge states in fractional quantum Hall systems by Jack polynomial. https://doi.org/10.1103/physrevb.89.165124

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