Topologically ordered states are quantum states of matter with topological ground-state degeneracy and quasiparticles carrying fractional quantum numbers and fractional statistics. The topological spin ${\theta }_a=2\pi h_a$ is an important property of a topological quasiparticle, which is the Berry phase obtained in the adiabatic self-rotation of the quasiparticle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose an approach to compute the topological spin and chiral central charge in lattice models by defining a quantity that we call the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a “partial translation operator.” We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Results are obtained for two example 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 a variational Monte Carlo wave function, which verify the analytic formula with high accuracy and further suggest that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides an efficient approach to extract characteristic quantities of topological states of matter from finite size numerics.

• Received 31 December 2012

DOI:https://doi.org/10.1103/PhysRevB.88.195412