We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian topological spin liquids. The Abelian anyons in the toric code include fermionic and bosonic quasiparticle excitations which see each other as π fluxes; namely, they result in the accumulation of a π phase if wound around each other. Non-Abelian behavior emerges because the Floquet modulation can engineer a nontrivial band topology for the fermions, inducing their fractionalization into Floquet-Majorana modes bound to the bosons. The latter then develop non-Abelian character akin to vortices in topological superconductors, realizing Ising topological order. Our findings shed light on the nonequilibrium physics of driven topologically ordered quantum matter and may facilitate the observation of non-Abelian behavior in engineered quantum systems.
We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian topological spin liquids. The Abelian anyons in the toric code include fermionic and bosonic quasiparticle excitations which see each other as π fluxes; namely, they result in the accumulation of a π phase if wound around each other. Non-Abelian behavior emerges because the Floquet modulation can engineer a nontrivial band topology for the fermions, inducing their fractionalization into Floquet-Majorana modes bound to the bosons. The latter then develop non-Abelian character akin to vortices in topological superconductors, realizing Ising topological order. Our findings shed light on the nonequilibrium physics of driven topologically ordered quantum matter and may facilitate the observation of non-Abelian behavior in engineered quantum systems.
Understanding topological matter is an outstanding challenge across several disciplines of physical science.Programmable quantum simulators have emerged as a powerful approach to studying such systems.While quantum spin liquids of paradigmatic toric code type have recently been realized in the laboratory, controlled exploration of topological phases with non-Abelian excitations remains an open problem.We introduce and analyze a new approach to simulating topological matter based on periodic driving.Specifically, we describe a model for a so-called Floquet spin liquid, obtained through a periodic sequence of parallel quantum gate operations that effectively simulates the Hamiltonian of the non-Abelian spin liquid in Kitaev's honeycomb model.We show that this approach, including the toolbox for preparation, control, and readout of topological states, can be efficiently implemented in state-of-the-art experimental platforms.One specific implementation scheme is based on Rydberg atom arrays and utilizes recently demonstrated coherent qubit transport combined with controlled-phase gate operations.We describe methods for probing the non-Abelian excitations, and the associated Majorana zero modes, and simulate possible fusion and braiding experiments.Our analysis demonstrates the potential of programmable quantum simulators for exploring topological phases of matter.Extensions including simulation of Kitaev materials and lattice gauge theories are also discussed.
We propose a scheme to implement Kitaev's honeycomb model with cold atoms, based on a periodic (Floquet) drive, in view of realizing and probing non-Abelian chiral spin liquids using quantum simulators.We derive the effective Hamiltonian to leading order in the inverse-frequency expansion, and show that the drive opens up a topological gap in the spectrum without mixing the effective Majorana and vortex degrees of freedom.We address the challenge of probing the physics of Majorana fermions, while having access only to the original composite spin degrees of freedom.Specifically, we propose to detect the properties of the chiral spin liquid phase using gap spectroscopy and edge quenches in the presence of the Floquet drive.The resulting chiral edge signal, which relates to the thermal Hall effect associated with neutral Majorana currents, is found to be robust for realistically prepared states.By combining strong interactions with Floquet engineering, our work paves the way for future studies of non-Abelian excitations and quantized thermal transport using quantum simulators.
Periodically driven quantum many-body systems support anomalous topological phases of matter, which cannot be realized by static systems. In many cases, these anomalous phases can be many-body localized, which implies that they are stable and do not heat up as a result of the driving. What types of anomalous topological phenomena can be stabilized in driven systems, and in particular, can an anomalous phase exhibiting non-Abelian anyons be stabilized? We address this question using an exactly solvable, stroboscopically driven 2D Kitaev spin model, in which anisotropic exchange couplings are boosted at consecutive time intervals. The model shows a rich phase diagram which contains anomalous topological phases. We characterize these phases using weak and strong scattering-matrix invariants defined for the fermionic degrees of freedom. Of particular importance is an anomalous phase whose zero flux sector exhibits fermionic bands with zero Chern numbers, while a vortex binds a pair of Majorana modes, which as we show support non-Abelian braiding statistics. We further show that upon adding disorder, the zero flux sector of the model becomes localized. However, the model does not remain localized for a finite density of vortices. Hybridization of Majorana modes bound to vortices form ``vortex bands,'' which delocalize by either forming Chern bands or a thermal metal phase. We conclude that while the model cannot be many-body localized, it may still exhibit long thermalization times, owing to the necessity to create a finite density of vortices for delocalization to occur.
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 non-Abelian anyons by an external field remain challenging as this field violates the exact solvability of the Kitaev model. Moreover, such a field to control non-Abelian 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. In particular, we find that a vison can be moved in a desired direction by using time-dependent local magnetic fields or gradient magnetic 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 topological quantum computation.
We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute the SO(N) Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedral Dk symmetry of SO(2n)1 , and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the C/G twist liquids, where G=Z2 for C=U(1)l , SU(n)1 , and G=Z2 , Zk , Dk for C=SO(2n)1 . We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern in SO(2n)1/G by identifying the non-chiral components of the twist liquids with discrete gauge theories.