Continuum limit of lattice quasielectron wavefunctions
Abstract
The charged local anyonic excitations of the fractional quantum Hall effect  the quasihole and the quasielectron  are created by adding or removing a magnetic flux. The existing trial wavefunctions of the quasielectron have several problems, such as lack of screening or wrong braiding properties. It was shown, however, that for lattice fractional quantum Hall systems, it is possible to find a relatively simple quasielectron wavefunction that has all the desired properties [New J. Phys. 20, 033029 (2018)]. This naturally poses the question: what happens to this wavefunction in the continuum limit? Here we demonstrate that, although one obtains a finite continuum wavefunction when the quasielectron is on top of a lattice site, such a limit of the lattice quasielectron does not exist in general. In particular, if the quasielectron is put anywhere else than on a lattice site, the lattice wavefunction diverges when the continuum limit is approached. The divergence can be removed by projecting the state on the lowest Landau level, but we find that the projected state does also not have the desired properties. We hence conclude that the lattice quasielectron wavefunction does not solve the difficulty of finding good trial states for quasielectrons in the continuum.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.12205
 Bibcode:
 2020arXiv200412205P
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 12 pages, 7 figures