Harvard Condensed Matter Theory Seminars

Csaba Toke, Penn State University

Recent results on the fractional quantum Hall effect at 5/2

The FQHE at half-filled second Landau level (5/2 and 7/2) has been a long standing enigma. The popular Pfaffian model of Moore and Read, applied to the 5/2 FQHE by Greiter, Wen, and Wilczek, is reviewed and scrutinized. In a exact diagonalization study on finite systems I show that the Pfaffian model provides an inaccurate description of the excitations, whose non-Abelian braiding statistics has been exploited in several quantum computing hardware proposals. I present an alternative understanding of the 5/2 FQHE within the composite fermion theory without the Pfaffian. I argue that the residual interaction between composite fermions plays a crucial role in establishing incompressibility at 5/2. The low-energy spectrum and the activation gap are estimated with the help of a pertubative procedure that incorporates inter-composite-fermion interactions. This approach is amenable to systematic perturbative improvements, and produces ground as well as excited states. It, however, does not relate to non-Abelian statistics in any obvious manner.

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