Density Functional Theory of the Abelian Anyon Gas

A Kohn-Sham density functional theory of composite fermions takes into account the flux attached to composite fermions in a self-consistent fashion [1]. We extend this method to treat a system of many anyons. We construct a series of states that do not involve the center of mass excitations, and explore behavior in the vicinity of the fermionic statistics. We compare the energy obtained from our DFT calculation with exact energies known for small systems and find a qualitative and semi-quantitative agreement. Our method provides an understanding of the existing exact result and also a self-consistent way to calculate the ground state properties of the anyon gas in the thermodynamic limit.

[1] Yayun Hu and J. K. Jain, Phys. Rev. Lett. 123, 176802(2019)