Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• Topological Quantum Matter

Background:

• Topologically ordered systems host exotic quasiparticles called anyons.
• Abelian anyons are well-understood, but non-Abelian anyons are key for topological quantum computing.
• Creating non-Abelian anyons from simpler systems is a significant challenge.

Purpose of the Study:

• To demonstrate the emergence of non-Abelian anyons from an Abelian topological system.
• To explore the effects of time-periodic driving (Floquet engineering) on topological phases.
• To realize Ising topological order in a controllable quantum system.

Main Methods:

• Utilizing the toric-code model as a representative Abelian topological system.
• Applying local time-periodic driving (Floquet modulation) to the system.
• Analyzing the fractionalization of fermionic quasiparticles into Floquet-Majorana modes.

Main Results:

• Non-Abelian anyons emerge from the Abelian toric-code model under Floquet driving.
• Floquet modulation engineers nontrivial band topology for fermions.
• Fermions fractionalize into Floquet-Majorana modes bound to bosons, realizing Ising topological order.

Conclusions:

• Non-Abelian anyons can be engineered from Abelian topological states using nonequilibrium methods.
• This work provides a pathway for observing non-Abelian behavior in quantum systems.
• Findings contribute to understanding the nonequilibrium physics of driven topological quantum matter.