Institute for Condensed Matter Theory Seminar: "Can Majorana fermions survive in isolation?"
- Sponsor
- The Institute for Condensed Matter Theory
- Speaker
- Ivar Martin, Argonne National Laboratory
- Views
- 115
Majorana zero modes are the simplest example of non-Abelian anyons. The promise of their realization in condensed matter systems led to the proposals to use them for topological quantum computing and even for teleportation.
The appearance of Majoranas in p-wave superconductors is well understood at the level of BCS mean-field theory; yet, it has proven extremely challenging to unambiguously detect these exotic particles in an experiment. Besides materials issues and other technical difficulties, it has been conjectured that perhaps the mean-field construction of Majoranas may be too naive, and a careful analysis of number-conserving interacting models and their true many-body eigenstates may be needed.
In this talk, I will examine the many-body number-conserving version of the mean-field Kitaev ground state. I will show that some but not all observables associated with Majoranas indeed survive the number-fixing procedure. I will also show how to construct a number-conserving version of the Majorana operator, which happens to agree with the conjecture recently made by Leggett. I will also present a test of teleportation in the presence of Coulomb interaction which partially imposes number conservation. Finally, I will discuss the prospects for numerically realizing Majorana braiding in the number-conserving setting.