  Recent experimental and numerical evidence suggest an intriguing universal
relationship between the Fermi surface anisotropy of the non-interacting parent
two-dimensional electron gas and the strongly correlated composite Fermi liquid
formed in a strong magnetic field close to half-filing. Inspired by these
observations, we explore more generally the question of anisotropy
renormalization in interacting 2D Fermi systems. Using a recently developed
non-perturbative and numerically-exact projective quantum Monte Carlo
simulation as well as other numerical and analytic techniques, only for Dirac
fermions with long-range Coulomb interactions do we find a universal
square-root decrease of the Fermi-surface anisotropy. For the half-filled
composite Fermi liquid, this result is surprising since a Dirac fermion ground
state was only recently proposed as an alternative to the usual HLR state. The
importance of the long-range interaction, expected for Dirac systems, is also
consistent with recent transport measurements. Our proposed universality can be
tested in several anisotropic Dirac materials including graphene, topological
insulators organic conductors, and magic-angle twisted bilayer graphene.
