We study the response of a Kitaev spin liquid (KSL) to a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamical excitation of a flux pair in the spin liquid and the system can be described by a generally particle-hole asymmetric interacting resonant level model. The dynamical excitation of the flux pair closes the flux gap in the spectrum of the spin correlation function locally for the gapless KSL even from the perturbative response to a weak magnetic field. Beyond the perturbative regime, the p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic and antiferromagnetic Kitaev couplings of the ground state and leads to very different behaviors for the two cases. The antiferromagnetic case experiences a first-order phase transition to the polarized state during magnetization, whereas the ferromagnetic case does not. This study can be generalized to the Kitaev model in a uniform magnetic field and may help understand issues in recent experiments on KSL candidates.
Quantum spin liquids (QSLs) host a variety of fractionalized particles. In Kitaev's paradigmatic honeycomb model a spin-fractionalizes intoflux due to emergentgauge field and matter Majorana fermions. Although these excitations have well-defined dynamics in the integrable limit, their direct experimental identification is notoriously challenging: realistic materials inevitably host additional symmetry-allowed interactions that break integrability and hybridize gauge and matter sectors, while magnetic fields, which are often required to suppress competing order and stabilize a putative QSL regime, further entangle the responses of different fractionalized quasiparticles and may even drive the system into field-induced spin-liquid phases that are not adiabatically connected to the integrable limit. A prominent example is the quantum Majorana metal, in which the distinct dynamics of fractionalized Majorana fermions can become directly visible in scattering. This review highlights recent progress on these related questions: in which field-stabilized QSL regimes and nearby emergent phases, and under what conditions, can the response of a specific fractionalized quasiparticle be isolated and positively understood, thereby clarifying the existence and the experimental scope of putative spin liquids? We review the progress on these questions across Abelian, non-Abelian, and emergent quantum phases under magnetic field that are not perturbatively connected to the integrable limit. We connect these field-induced dynamical phenomena to concrete experimental observables, relevant for neutron scattering, resonant inelastic x-ray scattering, and pump-probe spectroscopy, techniques that are capable of identifying the nature of different magnetic-field-induced phases and resolving specific types of fractionalized particles, including Majoranas andfluxes.
Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.
While phase transitions between magnetic analogs of the three states of matter-a long-range ordered state, paramagnet, and spin liquid-are extensively studied, the possibility of "liquid-liquid" transitions, namely, between different spin liquids, remains elusive. By introducing the additional Ising coupling into the honeycomb Kitaev model with bond asymmetry, we discover that the Kitaev spin liquid turns into a spin-nematic quantum paramagnet before a magnetic order is established by the Ising coupling. The quantum phase transition between the two liquid states accompanies a topological change driven by fractionalized excitations, the Z_{2} gauge fluxes, and is of first order. At finite temperatures, this yields a persisting first-order transition line that terminates at a critical point located deep inside the regime where quantum spins are fractionalized. It is suggested that similar transitions may occur in other perturbed Kitaev magnets with bond asymmetry.
Motivated by growing evidence for the significance of the third-nearest-neighbor Heisenberg (
J3) interaction in candidate Kitaev materials, we investigate the dynamical properties of the Kitaev spin liquid (KSL) under a
J3 perturbation, focusing on its spin dynamical structure factor (DSF) and Raman scattering. Within a self-consistent parton mean-field plus random-phase approximation framework, we find that
J3 induces coherent, paramagnon-like collective modes that coexist with a high-energy Majorana continuum in the spin DSF. The softening of these modes with increasing
∣J3∣ signals a quantum phase transition to magnetic order. Remarkably, magnetic ordering sets in at a common critical
J3 for both ferromagnetic (
K<0) and antiferromagnetic (
K>0) Kitaev models, with the resulting ordered states forming exact dual pairs under a four-sublattice duality transformation that maps
(K,J3)→(−K,J3). An external magnetic field further softens the preexisting paramagnon modes, thereby enhancing magnetic order. Perturbative Raman calculations show that while the Kitaev-like Raman vertex probes only itinerant matter Majorana fermions, the response from the
J3-like vertex features both matter Majoranas and visons. Four-vison excitations produce a sharp peak accompanied by a two-fermion continuum, whereas two-vison excitations yield a continuum closely resembling the single-matter-fermion density of states. These results provide a unified perspective on the dynamical signatures of
J3-perturbed KSL and are helpful for interpreting experimental spectra in candidate Kitaev materials with sizable
J3 interactions.
We investigate magnetic-field-induced transitions in the dynamical spin correlation functions of the Kitaev spin liquid (KSL). Using time-dependent Majorana mean-field theory, we show that in the ferromagnetic KSL, the real-space propagation of spin correlations evolves from isotropic to highly anisotropic with increasing field strength. Notably, the anisotropy emerges as a unidirectional propagation of spin correlations, whose direction is dictated by the orientation of the magnetic field relative to the underlying Kitaev bond geometry. We analyze this phase transition through both a Majorana mean-field framework and perturbative approach, and propose some experimental signatures and possible detection schemes. We further demonstrate that a similar transition occurs in the antiferromagnetic KSL, and discuss why previous studies focusing on the [111] field direction have overlooked this phenomenon, which further suggests the possibility to identify such anisotropic dynamics in candidate Kitaev materials.