Abstract
A model of the non-Abelian fractional quantum Hall effect is obtained from the diagonalization of the matrix model proposed by Dorey, Tong, and Turner (DTT). The Hamiltonian is reminiscent of a spin Calogero-Moser model but involves higher-order symmetric representations of the non-Abelian symmetry. We derive the energy spectrum and show that the Hamiltonian has a triangular action on a certain class of wave functions with a free-fermion expression. We deduce the expression of the ground-state eigenfunctions and show that they solve a Knizhnik-Zamolodchikov equation. Finally, we discuss the emergence of Kac-Moody symmetries in the large- limit using the level-rank duality, and we confirm the results obtained previously by DTT.
- Received 25 January 2024
- Revised 28 March 2024
- Accepted 2 April 2024
DOI:https://doi.org/10.1103/PhysRevB.109.155158
©2024 American Physical Society