Bosonisation of quasiholes and transmutation of braiding statistics in fractional quantum Hall states

We investigate the robustness of fractional braiding statistics of quasiholes in fractional quantum Hall (FQH) states. On the one hand, it is commonly believed that the quasiholes of FQH state at 1/m filling exhibit a braiding phase of 2π/3. On the other hand, there exist a one-to-one mapping between the Hilbert space of a model FQH state and the Hilbert space of bosons. This “bosonisation” scheme[1] implies that it is possible to construct an FQH state whose quasihole exhibit bosonic statistics. We show very high overlaps between the bosonic and anyonic states when the particle separation is large, indicating their energy difference can be very small. We emphasize that since the braiding statistics is a result of fluctuations in the electron density profile, the braiding phase measured in experiments is very sensitive to the exact shape of the quasihole packet, rather than a robust quantity as previously thought. Our analysis also suggests that it may be possible to observe fractional statistics in the (relatively) simple bosonic systems in a single Landau level. We propose an experimental scheme to realize these anyonic few-particle states.

References

[1] Bo Yang, Phys. Rev. Lett. 127, 126406 (2021).