Laughlin wavefunction

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In condensed matter physics, the Laughlin wavefunction is an ansatz for the ground state of some electrons placed in a uniform background magnetic field in the presence of a uniform jellium background when the filling factor of the lowest Landau level is 1/n where n is an odd positive integer. Being an ansatz, it's not exact, but qualitatively, it reproduces many features of the exact solution and quantitatively, it is pretty good.

If we ignore the jellium and mutual Coulomb repulsion between the electrons as a zeroth order approximation, we have an infinitely degenerate lowest Landau level and with a filling factor of 1/n, we'd expect that all of the electrons would lie in the LLL. Turning on the interactions, we can make the approximation that all of the electrons lie in the LLL. If Ψ is the wavefunction of the LLL state with the lowest orbital angular momentum, then the Laughlin ansatz is

\left[ \prod_{N \geqslant i \geqslant j \geqslant 1}\left( z_i-z_j \right)^n \right] \prod^N_{k=1}\psi(z_k)

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