Quaternion representation of FQHE wave functions: Search for instability near half-filling

Following Boyle’s work on monopole harmonics [1], we show that a unit quaternion representation of the Jain FQHE wave functions more elegantly captures behavior under rotation. The quaternion representation dramatically simplifies the Jain-Kamilla projection into the lowest Landau level [2], making it possible to study fractional states along the sequence ν = n/(2n+1) up to 17/35 and beyond for systems with up to 400 electrons. As a first application of this approach, we search for magnetoroton instability in wide quantum wells along the Jain sequence ν=n/(2n+1) as it approaches the CF Fermi Sea at ν=1/2.



[1] M. Boyle, How Should Spin-Weighted Spherical Functions Be Defined?, J. Math. Phys.57, 092504 (2016).

[2] J. K. Jain and R. K. Kamilla, Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level, Int. J. Mod. Phys. B 11, 2621 (1997).