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Digital quantum simulations of Kitaev’s honeycomb model are realized for two-dimensional fermionic systems using a reconfigurable atom-array processor and used to study the Fermi–Hubbard model on a square lattice.

An ultra-low-loss integrated photonic chip fabricated on a customized multilayer silicon nitride 300-mm wafer platform, coupled over fibre with high-efficiency photon number resolving detectors, is used to generate Gottesman–Kitaev–Preskill qubit states.

Recently, material realizations of the spin 3/2 Kitaev honeycomb model have been proposed, but the model has not been solved by either analytical or numerical methods. Here the authors report exact results for the spin 3/2 model consistent with numerical simulations, and find gapped and gapless quantum spin liquids.

A three-site Kitaev chain, constructed from three semiconducting quantum dots coupled by superconducting segments in a hybrid InSb/Al nanowire, shows enhanced robustness of edge zero-energy modes against variations in the coupling strengths or electrochemical potentials compared with a chain containing only two quantum dots.

Recent theoretical studies indicate that the Kitaev model may be realized in framework materials exhibiting extended superexchange pathways. Here the authors report experimental evidence showing that the material requirements for a Kitaev quantum spin liquid are satisfied in a inorganic framework material.

Previous numerical work has predicted a new spin liquid phase in the antiferromagnetic Kitaev model at intermediate magnetic fields; however, its nature is not easily discernible by numerical approaches. Here, by using a variational approach, the authors show that this phase is a gapped Abelian spin liquid

Geometric frustration and bond-dependent interactions each introduce quantum fluctuations that can create spin liquid phases. Now it is shown that CoI₂ is a triangular lattice material that combines both.

Na₃Ni₂BiO₆ with a honeycomb lattice is found to host a one-third magnetization plateau phase signifying frustrated interactions and indicates that Kitaev interactions can be realized in high-spin magnets.

RuCl₃ has stood out as a prime candidate in the search for quantum spin liquids; however, its antiferromagnetic ordering at low temperature suggests deviations from typical QSL models. Here, using resonant inelastic x-ray scattering, the authors provide a comprehensive determination of the low energy effective Hamiltonian.

Honeycomb lattices of divalent, high-spin Co ions are predicted to host dominant Kitaev exchange interactions expanding opportunities to realize the elusive Kitaev Quantum Spin Liquid (KQSL) state. Hydrostatic pressure studies on leading candidate material Na₃Co₂SbO₆ revealed a transition into a low-spin Co state, quenching the orbital degrees of freedom necessary to realize a KQSL state, but leading to possible emergence of quantum paramagnetism in the compressed honeycomb lattice of S=1/2 divalent Co ions.

α-RuCl₃ has properties consistent with predictions of a phase hosting fractionalized Majorana fermions but that could also be explained by conventional magnetic excitations. Here the authors find evidence for fractionalized quasiparticles by studying magnetic excitations across the field-temperature phase diagram.

It was recently proposed that the coupling between phonons and fractional excitations of a Kitaev quantum spin liquid can be detected in its phonon dynamics. Here, the authors report signatures of this coupling, manifested in low-energy phonon anomalies measured by inelastic X-ray scattering with meV resolution.

Kitaev materials are synonymous with quantum spin liquids, where due to a mix of different exchange interactions, they can house a range of exotic magnetic phenomena. Here, using a quantum chemical computational approach, the authors demonstrate the potentially important role anisotropic Coulomb exchange plays in the magnetic interactions of different Kitaev spin liquid candidate materials.

The authors report a strongly temperature-dependent thermal conductivity at low temperature, consistent with topological bosonic modes in a Chern-insulator-like model.

Inelastic neutron scattering characterization shows that α-RuCl₃ is close to an experimental realization of a Kitaev quantum spin liquid on a honeycomb lattice. The collective excitations provide evidence for deconfined Majorana fermions.

A minimal artificial Kitaev chain can be realized by using two spin-polarized quantum dots in an InSb nanowire strongly coupled by both elastic co-tunnelling and crossed Andreev reflection.

The antiferromagnetic spin 1/2 Kitaev model is known to have an intermediate phase under a magnetic field before transitioning to a fully polarized state. However, the nature of this phase for higher spins remained unclear. This paper explores the quantum phase diagram of the antiferromagnetic Kitaev honeycomb model in a magnetic field using tensor-network methods and high-order linked cluster expansions, uncovering an intermediate phase with distinct local magnetization patterns across different spin values.

α-RuCl₃ is a promising candidate for realizing the Kitaev quantum spin liquid, but the physics governing its magnetic behaviour remain elusive. Resonant elastic X-ray scattering data now set unambiguous constraints on the leading terms in the Hamiltonian.

The Kitaev quantum spin liquid is an exotic phase of matter exhibiting long-range entanglement and emergent Majorana fermions. This Review summarizes the concept and recent progress in realizing Kitaev model physics in transition metal compounds.

The mechanism behind the transient emergence of superconductivity upon irradiation with light in some materials is highly debated, which is in part due to the strong correlations at play. Here, the authors investigate the dynamical emergence of superconductivity in the strongly correlated, yet exactly solvable, Yukawa-Sachdev-Ye-Kitaev model and discuss differences and similarities to the relaxation dynamics of conventional superconductors.

A superconducting quantum computer is used to realize an out-of-equilibrium topologically ordered state, which hosts anyonic excitations.

Recent work proposed to search for quantum spin liquid in honeycomb cobaltates. Here the authors identify Cu₃Co₂SbO₆ as a promising candidate for quantum spin liquid research, revealing bond-dependent frustrated magnetism and robust spin fluctuations in the unconventional paramagnetic region via optical spectroscopy.

The Kondo effect from magnetic impurities has been proposed as a probe of fractionalized excitations in a topological quantum spin liquid. Lee et al. experimentally demonstrate the Kondo effect in a Kitaev candidate material α-RuCl3 with dilute Cr impurities.

Fractional excitations in quantum spin systems lead to exotic particles predicted in theory but difficult to observe in experiments. Here, Glamazda et al. report the dynamical Raman response of β- and γ-Li₂IrO₃is dominated by thermal damping of fermionic excitations, suggesting the emergence of Majorana fermions from spin fractionalization.

Kitaev interactions on a honeycomb lattice can potentially lead to a quantum spin liquid state. Unfortunately, materials hosting Kitaev interactions also host Heisenberg interactions favouring long range order. Here, Sakrikar, Shen, Poldi and coauthors find that the relative strength of the Heisenberg and Kitaev interactions can be tuned by pressure in Ag₃LiRh₂O₆.

Recently topological phases have been generalized to amorphous materials, but demonstrations have been limited to non-interacting particles. Cassella et al. show the emergence of chiral amorphous quantum spin liquid in an exactly soluble model by extending the Kitaev honeycomb model to random lattices.

Honeycomb iridates have been proposed as experimental realizations of the Kitaev model. An X-ray scattering study presents evidence for bond-directional interactions in Na₂IrO₃, a key requirement to make the connection with Kitaev physics possible.

The observation of magnetic excitation continua in putative Kitaev spin liquid compounds is consistent with predictions of exotic quantum behavior, attracting significant interest. Here, the authors show the observed continua could instead be a consequence of realistic non-Kitaev interactions.

Honeycomb iridates are candidates for the realization of a Kitaev spin liquid, displaying properties such as the protection of quantum information. Here, the authors investigate the phase diagram of honeycomb Li₂IrO₃, using quantum chemistry methods to derive the relevant effective spin Hamiltonian.

The authors study the formation and characteristics of a Majorana metallic quantum spin liquid state in Kitaev’s honeycomb model under a moderate external magnetic field. This state represents a novel class of gapless quantum spin liquids stabilized by magnetic field.

Kitaev quantum spin liquids are an exciting potential platform for hosting rich condensed matter physics. Here, the authors characterize the most promising material candidate, the honeycomb iridate H₃LiIr₂O₆ and reveal a broad continuum of collective excitations absent of a momentum dependence–suggestive of a disordered topological spin liquid.

The layered material α-RuCl₃ is a promising candidate for the Kitaev quantum spin liquid, but its low-temperature structure is debated. Here, using a new structural characterization approach, the authors report a pressure-induced high-symmetry phase in α-RuCl₃, which might be close to the ideal Kitaev geometry.

Two-dimensional honeycomb lattices of magnetic ions with strong spin-orbit coupling can host a rich variety of magnetic phases, including Kitaev quantum spin liquids. Here, Okuma et al succeeded in synthesising powders and single crystals of β-Na2PrO3, with Praseodymium ions with very strong spin-orbit coupling arranged in a three-dimensional hyperhoneycomb lattice.

Materials with a Kitaev spin liquid ground state are sought after as models of quantum phases but candidates so far form either zig-zag or incommensurate magnetic order. Ruiz et al. find a crossover between these states in β-Li₂IrO₃ under weak magnetic fields, indicating strongly frustrated spin interactions.

The creation and purification of magic states can be a limiting step in quantum computing. Now an error correcting code has been found where the overhead of this process is the lowest value possible, showing that optimal performance can be achieved.

The authors report a crossover from easy-plane to easy-axis magnetic anisotropy in monolayer RuCl₃, which they attribute to an in-plane distortion of the Cl atoms observed in electron diffraction that modify the non-Kitaev exchange terms. The results are useful for overcoming the challenge of realizing a quantum spin liquid.