A Review on the Applications of Density Functional Theory to the FQH System

The fractional quantum Hall (FQH) effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, fractionalized excitations, and anyonic statistics. Numerical simulations, such as exact diagonalization, density matrix renormalization group, matrix product states, and Monte Carlo methods, are essential to examine the properties of strongly correlated systems. Recently, density functional theory (DFT) has been employed in this field within the framework of composite fermion (CF) theory. In this paper, we assess how DFT addresses major challenges in FQH system, such as computing ground state and low-energy excitations. We emphasize the critical insights provided by DFT-based methods into the CF model, edge effects, and the nature of fractional charge and magnetoroton excitations. Furthermore, we examine the advantages and limitations of DFT approaches, highlight the interplay between numerical simulations and theoretical models. We finally discuss the future potential of time-dependent DFT (TDDFT) for modeling non-equilibrium dynamics.