Kohn-Sham density functional theory of Abelian anyons

Hu, Yayun; Murthy, G.; Rao, Sumathi; Jain, J. K.

doi:10.1103/physrevb.103.035124

Kohn-Sham density functional theory of Abelian anyons

Journal Article · Tue Jan 19 00:00:00 EST 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.035124· OSTI ID:1773674

^[1]; Murthy, G. ^[2]; ^[3]; ^[4]

Pennsylvania State Univ., University Park, PA (United States); Penn State
Univ. of Kentucky, Lexington, KY (United States)
Harish-Chandra Research Inst., Allahabad (India)
Pennsylvania State Univ., University Park, PA (United States)

In this work, we develop a density functional treatment of noninteracting 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 a few particles shows that the model captures the behavior qualitatively and semiquantitatively, 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.

View Accepted Manuscript (DOE)

Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0005042

OSTI ID:: 1773674

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 103; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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