|Heung-Sun Sim||Monday, 15:10 - 15:40|
|Nonlocal entanglement in 1D topological superconductor at finite temperature|
|In this talk, we discuss about nonlocal effects of non-Abelian anyons. First, we consider thermal states of 1D topological superconductors having Majorana zero modes at the ends . The thermal states can have nonlocal and length-independent entanglement in the bulk, depending on the number of the zero modes. In a superconductor having one Majorana zero mode at each end, nonlocal entanglement occurs in a Bell-state form at zero temperature, and decays as temperature increases, vanishing suddenly at certain finite temperature. In a superconductor having two zero modes at each end, it occurs in a cluster-state form and its nonlocality is more noticeable at finite temperature. The nonlocal entanglement results from the non-Abelian statistics of Majorana fermions and the fermion exchange statistics.
Second, we introduce a topologically connected Feynman diagram of anyons in 2D. This process involves topological braiding of virtually excited anyons around real anyonic excitations. It contributes to physical observables in the case of anyons, but not in fermions or bosons. It can be detected in a fractional quantum Hall system, providing a tool for experimental observation of anyonic braiding statistics. We develop a theory of the process for Abelian anyons  and non-Abelian anyons .
 Y. Park, J. Shim, S.-S. B. Lee, and H.-S. Sim, preprint (2017).
 C. Han et al., Nat. Commun. 7: 11131 (2016).
 C. Han and H.-S. Sim, preprint (2017).