Overlap of parafermionic zero modes at a finite distance
| Autor: | Teixeira, Raphael L. R. C., Haller, Andreas, Singh, Roshni, Mathew, Amal, Idrisov, Edvin G., da Silva, Luis G. G. V. Dias, Schmidt, Thomas L. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Phys. Rev. Research 4, 043094 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevResearch.4.043094 |
| Popis: | 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. Comment: 10 pages, 5 figures |
| Databáze: | arXiv |
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