[en] Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of Z2n parafermions which have been predicted to emerge as localized zero modes in fractional quantum Hall systems at filling factor ν=1/n (n odd). Using a combination of bosonization and refermionization, we calculate the energy splitting as a function of distance and chemical potential for a pair of parafermions separated by a gapped region. Braiding of parafermions in quantum Hall edge states can be implemented by repeated fusion and nucleation of parafermion pairs. We simulate the conventional braiding protocol of parafermions numerically, taking into account the finite separation and finite chemical potential. We show that a nonzero chemical potential poses challenges for the adiabaticity of the braiding process because it leads to accidental crossings in the spectrum. To remedy this, we propose an improved braiding protocol which avoids those degeneracies.
Disciplines :
Physics
Author, co-author :
Groenendijk, Solofo ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit
Calzona, Alessio; Institute of Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
Tschirhart, Hugo; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit
Idrisov, Edvin ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit
Schmidt, Thomas ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit
External co-authors :
yes
Language :
English
Title :
Parafermion braiding in fractional quantum Hall edge states with a finite chemical potential
Publication date :
25 November 2019
Journal title :
Physical Review. B, Condensed Matter and Materials Physics