interaction at $\nu=1/3$ is remarkably stable to variation in anisotropy. As we show below, in this range of $\alpha$, the ground state is described by a generalized Laughlin wavefunction. Moreover, the set of lowest neutral excitations, forming a magneto-roton branch, are also stable and separated from the rest of the spectrum. Within this manifold, some level crossings occur as $\alpha$ is changed, but this only corresponds to the redistribution of the levels within a roton branch. Beyond $\alpha \approx 0.5$, the ground-state energy rises, indicating an instability and the eventual destruction of the Laughlin phase.

![(Color online). Energy spectrum in units of $e^2/\epsilon l_B$ as a function of anisotropy $\alpha$ for the square unit cell and $n=0$ LL Coulomb interaction at $\nu=1/3$. The system is $N_e=7$ electrons and $\phi=0$. Due to the square unit cell, the spectrum is symmetric under $\alpha \rightarrow 1/\alpha$.[]{data-label="fig_onethirdenergy"}](anisolllsq_7_21.eps){width="0.7\linewidth"}

In rotationally-invariant situations, the incompressible liquids at fillings $\nu=1/m$ of $n=0$ LL ($m$ being an odd integer) are described by the Laughlin wavefunction [@laughlin]. In the geometry of an infinite plane, the Laughlin state is given by $$\label{laughlinwf}
\Psi_L^{\nu=1/m} = \prod_{i<j}(z_i-z_j)^m e^{-\sum_k z_k^* z_k/4\ell_B^2}.$$ Here $z=x+iy$ stands for the usual complex representation of the coordinates in the 