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Topologically ordered states are quantum states of matter with topologicalground state degeneracy and quasi-particles carrying fractional quantum numbersand fractional statistics. The topological spin $\theta_a=2\pi h_a$ is animportant property of a topological quasi-particle, which is the Berry phaseobtained in the adiabatic self-rotation of the quasi-particle by $2\pi$. Forchiral topological states with robust chiral edge states, another fundamentaltopological property is the edge state chiral central charge $c$. In this paperwe propose a new approach to compute the topological spin and chiral centralcharge in lattice models by defining a new quantity named as the momentumpolarization. Momentum polarization is defined on the cylinder geometry as auniversal subleading term in the average value of a "partial translationoperator". We show that the momentum polarization is a quantum entanglementproperty which can be computed from the reduced density matrix, and ouranalytic derivation based on edge conformal field theory shows that themomentum polarization measures the combination $h_a-\frac{c}{24}$ oftopological spin and central charge. Numerical results are obtained for twoexample systems, the non-Abelian phase of the honeycomb lattice Kitaev model,and the $\nu=1/2$ Laughlin state of a fractional Chern insulator described by avariational Monte Carlo wavefunction. The numerical results verifies theanalytic formula with high accuracy, and further suggests that this resultremains robust even when the edge states cannot be described by a conformalfield theory. Our result provides a new efficient approach to characterize andidentify topological states of matter from finite size numerics.

Momentum polarization: an entanglement measure of topological spin and chiral central charge