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Physica E Low-dimensional Systems and Nanostructures

Fixed-phase diffusion Monte Carlo study of the quantum-Hall effect on the Haldane sphere

V. Melik-Alaverdian, N. E. Bonesteel, Gerardo Ortíz

Published Jan 1, 1997• 2 citations
Publisher
DOI
10.1016/s1386-9477(97)00032-5

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A generalized diffusion Monte Carlo method for solving the many-body Schr\"odinger equation on curved manifolds is introduced and used to perform a ``fixed-phase'' simulation of the fractional quantum Hall effect on the Haldane sphere. This new method is used to study the effect of Landau level mixing on the $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3$ energy gap and the relative stability of spin-polarized and spin-reversed quasielectron excitations.
Pairing of composite fermions provides a possible mechanism for fractional quantum Hall effect at even denominator fractions and is believed to serve as a platform for realizing quasiparticles with non-Abelian braiding statistics. We present results from fixed-phase diffusion Monte Carlo calculations which predict that substantial Landau level mixing can induce a pairing of composite fermions at filling factors ν=1/2 and ν=1/4 in the l=-3 relative angular momentum channel, thereby destabilizing the composite-fermion Fermi seas to produce non-Abelian fractional quantum Hall states.