2012/04/30 by Shigehiro Yasui, Yuji Hirono, Kazunori Itakura +1 · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Advanced Condensed Matter Physics #Dirac fermion #Dirac sea #Dirac spinor #Fermion #Fermion doubling #Helical Dirac fermion #MAJORANA #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Vortex #cond-mat.supr-con #hep-ph #hep-th
paper · pdf · doi:10.1103/physreve.87.052142
published as Phys.Rev.E87:052142,2013 · 32 pages, no figures, v3: published version
openalex publication_date 2013/05/30 · arxiv created 2013/06/07 · arxiv updated 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.