  Recent years have seen the discovery of a chiral spin liquid state - a
bosonic analogue of a fractional Quantum Hall state first put forward by
Kalmeyer and Laughlin in 1987 - in several deformations of the Heisenberg model
on the Kagome lattice. Here, we apply state-of-the-art numerical techniques to
one such model, where breaking of the time-reversal symmetry drives the system
into the chiral phase. Our methods allow us to obtain explicit matrix-product
state representations of the low-lying excitations of the chiral spin liquid
state, including the topologically non-trivial semionic excitation. We
characterize these excitations and study their energetics as the model is tuned
towards a topological phase transition.
