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We find an exact spin liquid state without time reversal symmetry on thekagome lattice with odd number of electrons per unit cell and explicit wavefunctions for all eigenstates. We also obtain that all spin-spin correlationsare zero except trivial cases. We then show that there are anyonic excitationsin our model. Finally, we demonstrate the existence of ground state degeneracyand gapless edge states indicating nontrivial topological order in our model.We also label all eiginstates on torus by local and global string operators.

An exact spin liquid state on the kagome lattice with topological order