The celebrated Laughlin wave function

$$\psi_{\mathrm{Laughlin}}(z_1,\ldots,z_N) = \prod_{i<j} (z_i-z_j)^n\prod_i e^{-|z_i|^2/4}$$

is a (very good) approximation of the ground state of a two-dimensional electron gas in a uniform background magnetic field when the filling factor $\nu$ of the lowest Laundau level is equal to $1/n$ (for some odd integer $n$).

Now, I have a fundamental problem with this. The two-dimensional electron gas is obviously translation invariant (more precisely, invariant under the action of magnetic translations). So $\psi_{\mathrm{Laughlin}}$ should also be translation invariant. Clearly, as $N$ is a fixed finite integer, $\psi_{\mathrm{Laughlin}}$ cannot be translation invariant... but it should be *almost* translation invariant, and I just don't see why that should be the case.

Can someone please help me with that?