Response And Phase Transition Of A Kitaev Spin Liquid In A Local Magnetic Field

Quantum spin liquid(QSL)is a strongly correlated system with fascinating proper-ties,such as fractionalization,emergent topological order,long-range entranglement,etc.Since its original proposal as resonating valence bond liquid state,the search and study of QSL has attracted great efforts from both the the theorectical and experimental side.However,due to the lack of any local order,its identification is extremely difficult.Until about a decade ago,Kitaev proposed an exactly solvable minimal model on a 2D hon-eycomb lattice,which combines all the features of a QSL yet involves only nearest neighbor interactions on the lattice.This makes it possible to observe a Kitaev spin liq-uid(KSL)in artificial materials and cold atom systems.As one of the characteristic features of quantum spin liquid,the KSL exhibits frac-tionalized excitations of gauge fluxes and matter Majorana fermions.The initiating and probing of such fractionalized excitations often involves the dynamical response of the system.According to study of Konlle et al,the dynamical structure factor of the pure Kitaev model are known exactly and reveals the characteristic fractionalization of the KSL,e.g.,a flux gap in the spectrum of the dynamical structure factor appears even for the gapless KSL.In recent experimental search for proximate KSL in real materials,the candidates usually include not only Kitaev couplings but also the above Heisenberg orΓ and interactions,which induces a magnetic order at low temperature in the materi-als.To suppress the magnetic order,the experiments are often conducted in an external magnetic field.In this case,both the extra interaction and the magnetic field has sig-nificant impact on the dynamics of the fractionalized excitations.In this paper,we study the response of a Kitaev spin liquid(KSL)to a local mag-netic 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 full dynamics resembles that of a Kondo problem,but has totally different conse-quences compared to the conventional Kondo problem in metals.The p-h asymmetry plays a critical role for the finite Jz.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 perturba-tive regime,we use mean-field and NRG to further study.The p-h asymmetry cormpetes 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.