Extracting Topological Spins from Bulk Multipartite Entanglement

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory

Background:

• Topologically ordered phases are exotic states of matter characterized by long-range entanglement.
• Identifying these phases is crucial for understanding quantum materials and developing quantum technologies.

Purpose of the Study:

• To develop novel methods for identifying 2+1 dimensional topologically ordered phases.
• To introduce new entanglement measures capable of distinguishing between different topological phases.

Main Methods:

• Utilizing measurements on the ground-state wave function.
• Defining bulk multipartite entanglement measures based on permutation operators acting on multiple replicas of the wave function.
• Calculating topological invariants (quantum dimension and topological spin) of anyons.

Main Results:

• Introduced a series of entanglement measures that successfully extract topological invariants ∑_{a}d_{a}^{2}θ_{a}^{r} for nonchiral topological order.
• Demonstrated that these measures provide information beyond conventional methods like topological entanglement entropy.
• Showed that the proposed procedure is optimal in terms of the number of wave function replicas required.

Conclusions:

• The developed entanglement measures offer a powerful and refined tool for classifying topological phases of matter.
• The findings are generalizable to chiral topological states.
• This work advances the understanding of topological order and its detection.