Momentum Polarization: an Entanglement Measure of Topological Spin

Abstract

[evdate 2012-12-17] IAS Symposium on Frontiers in Condensed Matter Physics. Talk no.3

Title from title slide.

Abstract: Topologically ordered states are states of matter which are distinct from trivial states by topological properties such as ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by 2. The talk propose a new approach to compute the topological spin in candidate systems of two-dimensional topologically ordered states, and identify the topological spin with a new quantity, the momentum polarization defined on the cylinder geometry. The momentum polarization is determined by the quantum entanglement between the two halves of the cylinder, and can be computed from the reduced density matrix. As an example we present numerical results for the honeycomb lattice Kitaev model, which correctly reproduces the expected spin 1/16 of the Ising non-Abelian anyon. Th! e result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.

Duration: 34 min.