Fractional quantum Hall states reveal multi-anyon interactions and anisotropic impurity potentials A 2/5th electron charge energy splitting has been detected in fractional quantum Hall states, a phenomenon previously unobservable due to limitations in treating anyons as point-like objects. This splitting, observed at filling factors of 1/3 and 2/5, signifies a key threshold in understanding anyon behaviour, as prior methods lacked the sensitivity to resolve multi-anyon configurations trapped by impurities. The collaboration between Princeton University and the University of Leeds attributes this splitting to the complex interaction of multiple anyons confined within the electric potential of charged impurities. The fractional quantum Hall effect arises from the strong interaction between electrons in a two-dimensional electron gas subjected to a strong perpendicular magnetic field and low temperatures. This interaction leads to the formation of correlated many-body states with exotic properties, including the emergence of anyons. Unlike bosons or fermions, anyons exhibit fractional charge and obey exchange statistics differing from either of these conventional particle types; exchanging two identical anyons can alter the quantum state of the system. Numerical calculations reveal the effect requires an anisotropic, rather than rotationally symmetric, confining potential. A rotationally symmetric trap would eliminate the observed splitting entirely. The modelling at Princeton University and the University of Leeds confirmed the anisotropy of the confining potential, demonstrating that the energy splitting vanished entirely when a rotationally symmetric trap was simulated. This anisotropy arises from the specific arrangement of the charged impurity and the surrounding graphene lattice. The precise shape of the potential well created by the impurity dictates how the anyons distribute themselves, influencing their energy levels. The simulations employed sophisticated computational techniques, including density functional theory and exact diagonalization, to accurately model the many-body interactions and the confining potential. Further calculations revealed the competing multi-anyon states possess nearly identical charge