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It is known that the $m= 3$ Laughlin wave function is a very accurate approximation of the realistic ground state.

Is it the case that as $m $ increases, the Laughlin wave function as an approximation becomes less accurate and thus it becomes less relevant?

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Experiments observe quantized Hall plateaus corresponding to Laughlin-type states at $\nu = \tfrac{1}{3}$ and $\tfrac{1}{5}$, and the Laughlin wavefunction is a good description for both (though it may be a bit less accurate for the latter). However, the story is different for $m > 5$, $\nu = \tfrac{1}{7}, \tfrac{1}{9}, \cdots$. Plateaus either aren't observed at these small filling fractions, or they're absorbed into the neighboring IQHE plateau. For clean systems, it is believed that the electrons form a Wigner crystal, breaking translation symmetry, rather than a liquid state. So the Laughlin wavefunction is no longer an accurate description, even qualitatively.

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  • $\begingroup$ For $\nu = 1/7$, the magnetic field would be very high. Is it achievable experimentally? $\endgroup$
    – J.Bates
    Sep 26, 2016 at 2:17
  • $\begingroup$ Yes, it is a high but achievable field, see for example Phys. Rev. Lett. 61, 881 and the theoretical followup Phys. Rev. B 48, 11473 . Note the physics should be similar at filling $\nu = 1 + 1/m$, which is a lower field. $\endgroup$
    – mike
    Sep 26, 2016 at 2:36

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