Transition from Kitaev quantum spin liquid to weakly coupled critical spin chains*

We investigate quantum phase transitions in the Kitaev honeycomb model as a function of a magnetic field in the [001] direction and with bond anisotropy K_z/K with K_x=K_y=K. Using a combination of methods, exact diagonalization and density matrix renormalization group, and insights from mean field theory, we find four distinct phases as a function of (h,K_z/K): a gapless Kitaev spin liquid (KSL) at low anisotropy and low field, an intermediate gapless phase for a range of anisotropy K_z/K and h, the gapped Toric code phase at high anisotropy, and a trivial polarized phase. We show that the gapless to gapless transition between the KSL and the intermediate gapless phase is a Lifshitz transition driven by the change of occupation number of bond fermions. We further discover that the reduction of bond fermion occupation reduces the effective K_z coupling, resulting in weakly coupled chains that map to the critical Ising model in a transverse field. Approaching the intermediate gapless phase from high fields, linear spin wave theory performed in the polarized phase shows 1D boson modes dispersing only along the zigzag direction while having a flat band along the armchair direction.