Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the ferromagnetic Kitaev model but breaks down already inside this phase for the antiferromagnetic Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.
Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the ferromagnetic Kitaev model but breaks down already inside this phase for the antiferromagnetic Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.
We investigate the non-Abelian topological chiral spin liquid phase in the two-dimensional (2D) Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group (DMRG) and exact diagonalization (ED) we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for robust characterization. While the ferromagnetic (FM) Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy H∗FM≈0.02, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, H∗AFM≈0.2. Interestingly, for larger fields H∗AFM<H<H∗∗AFM, an intermediate gapless phase is observed, before a second transition to the high-field partially-polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. We discuss possible relevance of this result to RuCl3 under various magnetic fields.
We investigate the non-Abelian topological chiral spin-liquid phase in the two-dimensional Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group and exact diagonalization we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for a robust characterization. While the ferromagnetic Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy ${H}_{*}^{\text{FM}}\ensuremath{\approx}0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, ${H}_{*}^{\text{AFM}}\ensuremath{\approx}0.2$. Interestingly, for larger fields H∗AFM<H<H∗∗AFM, an intermediate gapless phase is observed, before a second transition to the high-field partially polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl3 under magnetic fields.
Kitaev's honeycomb model is a paradigmatic exactly solvable system hosting a quantum spin liquid with non-Abelian anyons and topologically protected edge modes, offering a platform for fault-tolerant quantum computation. However, real candidate Kitaev materials invariably include complex secondary interactions that obscure the realization of spin-liquid behavior and demand novel quantum computational approaches for efficient simulation. Here we report quantum simulations of a 22-site Kitaev honeycomb lattice on a trapped-ion quantum processor, without and with non-integrable Heisenberg interactions that are present in real materials. We develop efficient quantum circuits for ground-state preparation, achieving high accuracy with energy errors equivalent to an effective temperature of 0.2 (in units of the Kitaev interactions), consistent with the experimentally relevant spin-liquid regime. Starting from these states, we apply controlled perturbations and measure time-dependent spin correlations along the system's edge. In the non-Abelian phase, we observe chiral edge dynamics consistent with a non-zero Chern number, a hallmark of topological order, which vanishes upon transition to the Abelian toric code phase. Extending to the non-integrable Kitaev-Heisenberg model, we find that weak Heisenberg interactions preserve chiral edge dynamics, while stronger couplings suppress them, signaling the breakdown of topological protection. Our work demonstrates a viable route for probing dynamical signatures of topological order in quantum spin liquids using programmable quantum hardware, opening new pathways for quantum simulation of strongly correlated materials.
We compute the spectra of anyon quasiparticles in all three super-selection sectors of the Kitaev model (i.e., visons, fermions and bosons), perturbed by a Zeeman field away from its exactly solvable limit, to gain insights on the competition of its non-abelian spin-liquid with other nearby phases, such as the mysterious intermediate state observed in the antiferromagnetic model. Both for the ferro- and antiferro-magnetic models we find that the fermions and visons become gapless at nearly identical critical Zeeman couplings. In the ferromagnetic model this is consistent with a direct transition into a polarized state. In the anti-ferromagnetic model this implies that previous theories of the intermediate phase viewed as a spin liquid with a different fermion Chern number are inadequate, as they presume that the vison gap does not close. In the antiferromagnetic model we also find that a bosonic quasiparticle becomes gapless at nearly the same critical field as the fermions and visons. This boson carries the quantum numbers of an anti-ferromagnetic order parameter, suggesting that the intermediate phase has spontaneously broken symmetry with this order.
The Kitaev model exhibits a quantum spin liquid hosting emergent fractionalized excitations. We study the Kitaev model on the honeycomb lattice coupled to a magnetic field along the [111] axis. Utilizing large-scale matrix product-based numerical models, we confirm three phases with transitions at different field strengths depending on the sign of the Kitaev exchange: a non-Abelian topological phase at low fields, an enigmatic intermediate regime only present for antiferromagnetic Kitaev exchange, and a field-polarized phase. For the topological phase, we numerically observe the expected cubic scaling of the gap and extract the quantum dimension of the non-Abelian anyons. Furthermore, we investigate dynamical signatures of the topological and the field-polarized phase using a matrix product operator-based time evolution method.
Non-Abelian anyonic excitations of quantum spin liquids have potential for application to topological quantum computation, but designing logical operations requires developing protocols to faithfully create, move, and read out such quasiparticles. In this paper, we test two such protocols for manipulating Z 2 fluxes (“visons”) of ferromagnetic and antiferromagnetic Kitaev models perturbed by a small uniform magnetic field. We show that a protocol that employs a driving magnetic field locally applied to the sites of the lattice suffers from significant unavoidable errors. These errors, accumulating over time, prevent reaching high probabilities of generating and displacing flux pairs. However, individual spin couplings can also be turned on and off, thus it is possible to create and displace fluxes with nearly 100 % probability. We show that braiding non-Abelian anyons can be achieved with good precision with our second protocol. We comment on the feasibility of our protocols in solid-state devices and quantum emulators.