Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies

Abstract

We study the spin-one Kitaev model on the honeycomb lattice in the presence of single-ion anisotropies. We consider two types of single ion anisotropies: A D111 anisotropy which preserves the symmetry between X, Y and Z bonds but violates flux conservation and a D100 anisotropy that breaks the symmetry between X, Y and Z bonds but preserves flux conservation. We use series expansion methods, degenerate perturbation theory, and exact diagonalization to study these systems. Large positive D111 anisotropy leads to a simple product ground state with conventional magnon-like excitations, while large negative D111 leads to a broken symmetry and degenerate ground states. For both signs there is a phase transition at a small |D111| ≈ 0.2 separating the more conventional phases from the Kitaev Spin Liquid phase. With large D100 anisotropy, the ground state is a simple product state, but the model lacks conventional dispersive excitations due to the large number of conservation laws. Large negative D100 leads to decoupled one-dimensional systems and many degenerate ground states. No evidence of a phase transition is seen in our numerical studies at any finite D100. Convergence of the series expansion extrapolations all the way to D100 = 0 suggests that the non-trivial Kitaev spin-liquid is a singular-limit of this type of single-ion anisotropy going to zero, which also restores symmetry between X, Y and Z bonds.