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In quantum spin liquid states, the fractionalized spinon excitations cancarry fractional crystal symmetry quantum numbers, and this symmetryfractionalization distinguishes different topologically ordered spin liquidstates. In this work we propose a simple way to detect signatures of suchcrystal symmetry fractionalizations from the crystal symmetry representationsof the ground state wave function. We demonstrate our method on projected$\mathbb Z_2$ spin liquid wave functions on the kagome lattice, and show thatit can be used to classify generic wave functions. Particularly our method canbe used to distinguish several proposed candidates of $\mathbb Z_2$ spin liquidstates on the kagome lattice.

Detecting crystal symmetry fractionalization from the ground state: Application to $\mathbb Z_2$ spin liquids on the kagome lattice