Abstract
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.
| Original language | English |
|---|---|
| Article number | 035124 |
| Journal | Physical Review B |
| Volume | 103 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 19 2021 |
Bibliographical note
Funding Information:We thank G. J. Sreejith and Yinghai Wu for helpful discussions. The work at Penn State was made possible by financial support from the US Department of Energy under Grant No. DE-SC0005042. Y. H. acknowledges partial financial support from China Scholarship Council. The numerical calculations were performed using Advanced CyberInfrastructure computational resources provided by The Institute for CyberScience at The Pennsylvania State University. We thank the Indian Institute Science, Bangalore, where part of this work was performed, for their hospitality, and the Infosys Foundation for making the visit possible. We also thank International Centre for Theoretical Sciences, Bangalore, for its hospitality and support during the workshop “Novel phases of Quantum Matter,” where this work was initiated. G.M. acknowledges support under the US-Israel Binational Science Foundation Grant No. 2016130.
Funding Information:
We thank G. J. Sreejith and Yinghai Wu for helpful discussions. The work at Penn State was made possible by financial support from the US Department of Energy under Grant No. DE-SC0005042. Y. H. acknowledges partial financial support from China Scholarship Council. The numerical calculations were performed using Advanced CyberInfrastructure computational resources provided by The Institute for CyberScience at The Pennsylvania State University. We thank the Indian Institute Science, Bangalore, where part of this work was performed, for their hospitality, and the Infosys Foundation for making the visit possible. We also thank International Centre for Theoretical Sciences, Bangalore, for its hospitality and support during the workshop "Novel phases of Quantum Matter," where this work was initiated. G.M. acknowledges support under the US-Israel Binational Science Foundation Grant No. 2016130.
Publisher Copyright:
© 2021 American Physical Society.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics