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2007

An exact chiral spin liquid with non-Abelian anyons

Yao, Hong, Kivelson, Steven A.

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We establish the existence of a chiral spin liquid (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle.

The CSL state spontaneously breaks time reversal symmetry but preserves other symmetries.
There are two topologically distinct CSLs separated by a quantum critical point.
Interestingly, vortex excitations in the topologically nontrivial (Chern number $\pm 1$) CSL obey non-Abelian statistics.

An exact chiral spin liquid with non-Abelian anyons · Around

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There are 2 L y − 1 2^{L_{y}-1} gauge-like choices { U i j } \{U_{ij}\} on z ′ z^{\prime} -links consistent with the specified fluxes ( Φ → , { ϕ p } ) (\vec{\Phi},\{\phi_{p}\}) —here, L y L_{y} is the width of the system along y ^ \hat{y} direction. The eigenstate ψ ⁡ ( { U i j } ) \psi(\{U_{ij}\}) of the corresponding quadratic Hamiltonian is not

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