Reference : Overlap of parafermionic zero modes at a finite distance

	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Physics
	To cite this reference:	http://hdl.handle.net/10993/53110

Title :	Overlap of parafermionic zero modes at a finite distance
Language :	English
Author, co-author :	Teixeira, Raphael L. R. C. [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) > ; Universidade de São Paulo > Instituto de Física]
	Haller, Andreas [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) >]
	Singh, Roshni [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)]
	Mathew, Amal [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)]
	Idrisov, Edvin [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)]
	Dias da Silva, Luis G. G. V. [Universidade de São Paulo > Instituto de Física]
	Schmidt, Thomas [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) >]
Publication date :	14-Nov-2022
Journal title :	Physical Review Research
Publisher :	American Physical Society (APS)
Peer reviewed :	Yes
e-ISSN :	2643-1564
City :	College Park
Country :	United States - Maryland
Abstract :	[en] Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying $\mathbb{Z}_{2n}$ symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.
Permalink :	http://hdl.handle.net/10993/53110
DOI :	10.1103/PhysRevResearch.4.043094
Other URL :	https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.043094
Mentions required by the publisher for OA :	Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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