  A fractional quantum Hall (FQH) system with broken rotational symmetry
exploits its geometric degree of freedom to minimize its ground state energy.
The mass anisotropy of bare particles interacting isotropically is partially
inherited by the many-body FQH state, and the extent to which it does so
depends on the type of interaction, filling fraction and ground state phase.
Using numerical infinite density matrix renormalization group simulations, we
investigate the transference of elliptical ($C_2$-symmetric) anisotropy from
the band mass of the bare particles to the FQH states, for various power law
interactions. We map out the response of FQH states to small anisotropy as a
function of power law exponent, filling, and statistics (bosonic or fermionic)
of the constituents. Interestingly, we find a non-analyticity in the linear
response of the FQH state at a special filling-dependent value of the power law
exponent, above which the interaction effectively becomes zero-range
(point-like). We also investigate the the effect of $C_4$-symmetric band
distortions, where we observe a strikingly different dependence on filling.
