these can be tuned as free parameters. In the presence of anisotropy, however, the highest symmetry is only given by the rectangular lattice, even when $|\mathbf{a}|=|\mathbf{b}|$. Tuning the angle $\theta$ enables to perform the area-preserving deformations of the torus, which is useful in resolving the collective modes of FQH states in finite systems, and probing quantities such as Hall viscosity [@duncan].

In this paper we only consider spin polarized electrons and neglect the so-called multicomponent degrees of freedom, which can be the usual spin or bilayer/valley degree of freedom. This means that the filling factors we refer to as $n+\nu$ correspond to $kn+\nu$ in experiments, where integer $k$ denotes the additional degeneracy that comes from several “flavors" of electrons.

Anisotropy in the lowest Landau level: robustness and the intrinsic metric of the Laughlin state {#sec_laughlin}
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In Fig. \[fig\_onethirdenergy\], we present the energy spectrum of the Coulomb interaction at $\nu=1/3$ as a function of anisotropy (we assume $\phi=0$). The system is placed on the torus with a square unit cell, and energies are expressed in units of $e^2/\epsilon\ell_B$. A very flat minimum around isotropy point and the existence of a robust gap suggest that the ground state of the Coulomb 