Majorana representations of spin and an alternative solution of the Kitaev honeycomb model

2018/01/29 by Jianlong Fu, Johannes Knolle, Natalia B. Perkins · 1 citation
Physics and Astronomy · #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.97.115142

published as Phys. Rev. B 97, 115142 (2018) · 14 pages, 3 figure

arxiv created 2018/01/29 · arxiv updated 2018/03/28

Abstract

Based on the Dirac spinor representation of the SO(4) group, we discuss the relationship between three types of representation of spin in terms of Majorana fermions, namely the Kitaev representation, the SO(3) representation and the SO(4) chiral representation. Comparing the three types, we show that the Hilbert space of the SO(3) representation is different from the other two by requiring pairing of sites, but it has the advantage over the other two in that no unphysical states are involved. As an example of its application, we present a new alternative solution of the Kitaev honeycomb model. Our new solution involves no unphysical states which enables a systematic calculation of physical observables. Finally, we discuss an extension of the model to a more general exactly soluble Z₂ gauge theory interacting with complex fermions.

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