By P. Dirac

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**Additional info for Development of Quantum Theory: J. Robert Oppenheimer Memorial Prize Acceptance Speech**

**Example text**

8), and I show that for certain operators O is unnecessary because matrix elements hˆjPOPjˆi=hˆjOjˆi are independent of the projection. The four different Majorana fermions, Eq. 5), can be combined into two complex fermions, see Fig. 2 for an illustration. First, bond fermions (Baskaran et al. 2007; Yao et al. 1 Exact Solution and Projection by 27 bx χ yr b y bx c bz χ xr z fr χ r bz c bx b y χ xr−n 1 by bx χ yr−n 2 Fig. 2 The representation of spins in terms of four Majorana fermions is shown in the left.

As discussed in the introduction, fractionalization is another prominent feature of QSLs, similar to the appearance of the emergent gauge structure. All together, these features make the Kitaev model a prime example of a QSL. 3 Experimental Realization 33 exact solubility it has become the workhorse for model calculations of topologically ordered phases in 2D. The pure honeycomb model as described until now harbors gapless and gapped QSL phases, see Fig. 4, and its excitations can be shown to obey Abelian statistics (Kitaev 2006).

G. Radaelli, Y. Singh, P. R. -W. J. Baker, C. Stock, J. Taylor, Spin waves and revised crystal structure of honeycomb iridate Na2IrO3. Phys. Rev. Lett. V. Chubukov, T. Jolicoeur, Dimer stability region in a frustrated quantum Heisenberg antiferromagnet. Phys. Rev. B 44(21), 12050–12053 (1991) R. M. Hayden, G. G. D. E. -W. Cheong, Z. Fisk, Spin waves and electronic interactions in La2CuO4. Phys. Rev. Lett. 86(23), 5377–5380 (2001) L. Cooper, D. B. O. R. J. S. M. Kurn, W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms.