Dynamical response of the Kitaev quantum spin liquid in the $KJ\Gamma$-model under external magnetic field

We study the dynamical structure factor of the Kitaev quantum spin liquid (KQSL) generally, i.e. away from the solvable Kitaev limit, in the $KJ\Gamma$-model with external magnetic field. Using Majorana mean field theory, we compute spin susceptibility by including Majorana interactions in the random phase approximation (RPA). At zero field for the pure Kitaev model, RPA reproduces qualitatively spin susceptibility in the adiabatic approximation, which is close to the exact result. Small non-Kitaev couplings $J$ and $\Gamma$ induce sharp low-energy magnon modes as Majorana bound states. Larger couplings or finite field generally tend to weaken the KQSL and cause the sharp modes to condense, whence the system becomes magnetically ordered. However in specific paramter regimes, magnetic field may destroy the zero-field magnetic order and stabilize KQSL at intermediate field values, thus exemplifying the proposed `field-induced KQSL'.