Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation

Abstract

Quantum spin liquids realized in the Kitaev model offer a platform for fractionalization of spin into two quasiparticles: itinerant Majoranas and localized visons. Introducing a uniform weak magnetic field associates a Majorana zero mode with each vison excitation. The vison accompanied by a Majorana zero mode is known to behave as a non-Abelian anyon, which has garnered significant attention for its potential applications in topological quantum computing. Although spatial and temporal control of these anyons is essential for exploring their applicability in quantum computing, numerical simulations of creating, moving, and annihilating anyons by an external field remain challenging as this field violates the exact solvability of the Kitaev model. Moreover, such a field to control anyons may disturb the quantum state due to the energy injection it causes. In this study, by introducing energy dissipation phenomenologically in real-time simulations, we demonstrate that the generation, movement, and annihilation of vison excitations can be achieved while maintaining their localization. We find that a vison can be moved in a desired direction by using time-dependent local magnetic fields or gradient fields, and it remains accompanied by a Majorana zero mode even after its movement. We also reveal that a larger spatial extent of the Majorana zero modes bound to a vison facilitates the movement of the vison with smaller field gradients. Furthermore, our numerical simulations demonstrate pair creation and annihilation of visons, triggered by time-dependent magnetic fields. The results obtained in this study highlight the significance of energy dissipation in controlling non-Abelian anyons, which will stimulate further investigations into the nonequilibrium dynamics of fractional quasiparticles in strongly correlated electron systems, as well as studies for applications in quantum computation.

20 pages, 12 figures

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