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We develop a density functional treatment of non-interacting abelian anyons, which is capable, in principle, of dealing with a system of a large number of anyons in an external potential. Comparison with exact results for few particles shows that the model captures the behavior qualitatively and semi-quantitatively, especially in the vicinity of the fermionic statistics. We then study anyons with statistics parameter $1+1/n$, which are thought to condense into a superconducting state. An indication of the superconducting behavior is the mean-field result that, for uniform density systems, the ground state energy increases under the application of an external magnetic field independent of its direction. Our density-functional-theory based analysis does not find that to be the case for finite systems of anyons, which can accommodate a weak external magnetic field through density transfer between the bulk and the boundary rather than through transitions across effective Landau levels, but the Meissner repulsion of the external magnetic field is recovered in the thermodynamic limit as the effect of the boundary becomes negligible. We also consider the quantum Hall effect of anyons, and show that its topological properties, such as the charge and statistics of the excitations and the quantized Hall conductance, arise in a self-consistent fashion.
We present a rigorous formulation of generalized Kohn-Sham density-functional theory. This provides a straightforward Kohn-Sham description of many-body systems based not only on particle-density but also on any other observable. We illustrate the fo
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional
We construct exact Kohn-Sham potentials for the ensemble density-functional theory (EDFT) from the ground and excited states of helium. The exchange-correlation (XC) potential is compared with the quasi-local-density approximation and both single det
We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computati
In numerical computations of response properties of electronic systems, the standard model is Kohn-Sham density functional theory (KS-DFT). Here we investigate the mathematical status of the simplest class of excitations in KS-DFT, HOMO-LUMO excitati