Study On A Solvable One--dimensional Kitaev--Kondo Model

In recent years,Kitaev spin liquid materials such as Na₂Ir O₃and?-Rucl₃,have been a hot issue in condensed matter physics due to possible fractionalized excitation and non-trivial topological order.Theoretically,the ideal Kitaev model without Heisenberg interaction is exactly solvable,and its ground state is Kitaev spin liquid.When other interactions exist,generally,the model does not have exact analytical solution but only can be studied by numerical tools.If conduction electrons are coupled with local spins via Kondo coupling,Ki-taev model is extended to Kitaev-Kondo model.Currently,our understanding on this model is limited to crude mean-field approximations.In this thesis,we find that the one-dimensional Kitaev-Kondo model can be solved by bosonization in anisotropic limit.Further,we found that the phase diagrams computed with the Density Matrix Renormalization Group(DMRG)are basically the same as the Bose results.Specifically,we find:(1)When Kondo coupling is zero,the ground state is the fractionalized Fermi liquid;(2)When Kitaev coupling is isotropic,charge and spin excitation are gapless and the system is the heavy Fermi liquid;(3)When Kitaev coupling is anisotropic,spin excitation is gapped but charge is gapless,which indicates the Luther-Emery liquid.(4)When the lateral Kondo interaction is added,the Kitaev interaction dominates the magnetic effect of the system.Our work shows that the Kitaev physics always dominates in one dimension and should be helpful to understand possible metallic Kitaev materials in near future.