Verifying non-Abelian statistics by numerical braiding Majorana fermions

Recently, Majorana fermions have attracted intensive attention because of their possible non-Abelian statistics and potential applications in topological quantum computation. This paper describes an approach to verify the non-Abelian statistics of Majorana fermions in topological superconductors. From the relationship between the braiding operator of Majorana fermions and that of Bogoliubov-de Gennes states, we determine that Majorana fermions in one-dimensional and two-dimensional topological superconductors both obey non-Abelian statistics.