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We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice).
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Note that L = L x L=L_{x} , resp. L = L y L=L_{y} , for j e x ( top / bottom ) j_{ex}({\rm top/bottom}) , resp. j e x ( left / right ) j_{ex}({\rm left/right})
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Supplementary Material
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“–” in the last line means that the quantization κ x y f , expt \kappa_{xy}^{\rm f,expt} relative to κ x y q \kappa_{xy}^{\rm q} is not generic ( κ x y f , expt ≷ κ x y q \kappa_{xy}^{\rm f,expt}\gtrless\kappa_{xy}^{\rm q} ) in the weak coupling regime λ ≲ λ f \lambda\lesssim\lambda_{f} , i.e., it depends on the strength of λ \lambda and the position x x where the temperature is measured
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Using the Fourier transform definition η ( x ) = 2 L x ∑ k ≥ 0 ( η k e i k x + η k † e − i k x ) \eta(x)=\sqrt{\frac{2}{L_{x}}}\sum\displaylimits_{k\geq 0}\left(\eta_{k}e^{ikx}+\eta_{k}^{\dagger}e^{-ikx}\right) where the sum runs only over positive momenta, we obtain the same results
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The same conclusion can be obtained by calculating the matrix element diagrammatically [see Fig. 3
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