Abstract
We relate the Z2 gauge theory formalism of the Kitaev model to the SU(2) gauge theory of the resonating valence bond physics. Furthermore, we reformulate a known (Feng et al (2007 Phys. Rev. Lett. 98 087204), Chen and Hu (2007 Phys. Rev. B 76 193101), Chen and Nussinov (2008 J. Phys. A: Math. Theor. 41 075001) and Mandal et al (2006 Int. Conf. on Physics Near the Mott Transition)) Jordan–Wigner transformation of the Kitaev model on a torus in a general way that shows that it can be thought of as a Z2 gauge-fixing procedure. We give an explicit construction of the generators of large gauge transformations on a torus in terms of the spin operators. Using these and the non-trivial loop operators, we construct four mutually anti-commuting operators which commute with the Hamiltonian enabling us to prove that all eigenstates of this model, for the time-reversal symmetric case, are fourfold degenerate in the thermodynamic limit.
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