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Recent years have seen the discovery of a chiral spin liquid state - abosonic analogue of a fractional Quantum Hall state first put forward byKalmeyer and Laughlin in 1987 - in several deformations of the Heisenberg modelon the Kagome lattice. Here, we apply state-of-the-art numerical techniques toone such model, where breaking of the time-reversal symmetry drives the systeminto the chiral phase. Our methods allow us to obtain explicit matrix-productstate representations of the low-lying excitations of the chiral spin liquidstate, including the topologically non-trivial semionic excitation. Wecharacterize these excitations and study their energetics as the model is tunedtowards a topological phase transition.

Semion wave function and energetics in a chiral spin liquid on the Kagome lattice