Dynamics of Kitaev Spin Liquid under A Local Magnetic Field

We study the response of a gapless Kitaev spin liquid to a local magnetic field perpendicular to the 2D Kitaev lattice. The Kitaev spin liquid is well known to contain fractionalized excitations of flux and matter majorana fermions. A local magnetic field can not only excite a pair of flux and a majorana fermion, it also introduces a dynamics to the flux excitation. The system including the local magnetic field can be described by an interacting resonant level model. In ordinary metal this model can be mapped to a Kondo problem describing conduction electrons scattered by a magnetic impurity. However, unlike in metals, the density of states for matter fermions vanishes at Dirac points in gapless Kitaev spind liquid. This results in a residue entropy of ln2 of the pseudospin defined by bond fermion states in the Kitaev spin liquid at zero temperature, in contrast to the case in ordinary metal, where the entropy of magnetic impurity vanishes at zero T. This indicates that in opposite to the full screening of magnetic impurity in ordinary metals, there is no 'screening' of the pseudospin at all in the Kitaev spin liquid. At the end, a nonperturbative susceptibility of the spin liquid at both low and high magnetic field is obtained and studied.