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Journal Article

Fibonacci anyons and charge density order in the 12/5 and 13/5 quantum Hall plateaus


Pollmann,  Frank
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Mong, R. S. K., Zaletel, M. P., Pollmann, F., & Papic, Z. (2017). Fibonacci anyons and charge density order in the 12/5 and 13/5 quantum Hall plateaus. Physical Review B, 95(11): 115136. doi:10.1103/PhysRevB.95.115136.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-ADDD-4
The nu = 12/5 fractional quantum Hall plateau observed in GaAs semiconductor wells is a suspect in the search for non-Abelian Fibonacci anyons. Using the infinite density matrix renormalization group, we find clear evidence that fillings nu = 12/5 and nu = 13/5 are in the k = 3 Read-Rezayi phase in the absence of particle-hole symmetry breaking effects. The lowest energy charged excitation is identified as a non-Abelian Fibonacci anyon, distinguished from its Abelian counterpart by its local quadrupole moment. However, several experiments at nu = 13/5 observe a reentrant integer quantum Hall effect, implying particle-hole symmetry is broken. We rule out spin polarization as the origin of the asymmetry. Further, we point out extremely close energetic competition between the Read-Rezayi phase and a reentrant integer quantum Hall phase. This competition suggests that even small particle-hole symmetry breaking perturbations can explain the experimentally observed asymmetry between nu= 12/5 and 13/5. We find that at nu = 12/5 Landau level mixing favors the Read-Rezayi phase over the reentrant phase.