a given anisotropic ground state of a finite system.

An alternative way to obtain the intrinsic metric is to analyze the shape of the lowest excitation – the magneto-roton mode, which was successfully described by the single-mode approximation [@sma]. In a rotationally-invariant case, this mode has a minimum at $k \sim \ell_B^{-1}$. In the presence of anisotropy, the minimum occurs at different $|k|$ in the different directions (Fig. \[fig\_rotonaniso\]). This leads to an alternative definition of the intrinsic metric based on the shape of the roton minimum in the 2D momentum plane. We numerically establish that this definition agrees well with our previous definition of the intrinsic metric.

![(Color online). Energy spectrum of $N_e=9$ electrons at $\nu=1/3$ with the effective mass anisotropy $\alpha_m=2$ along the $x$-axis. When plotted as a function of $\sqrt{k_x^2+k_y^2}$ (green crosses), two branches of the magneto-roton mode are present (blue dotted lines are guide to the eye). If the spectrum is plotted as a function of $\sqrt{g^{ab}k_a k_b}$, the two branches collapse onto the same curve.[]{data-label="fig_rotonaniso"}](spa.eps){width="1\linewidth"}

In Fig. \[fig\_rotonaniso\] we plot the energy spectrum of an anisotropic Coulomb interaction at $\nu=1/3$ as a function of the rescaled momentum $\sqrt{g^{ab}k_a k_b}$, where $g$ is the guiding center 