Spin-1 Kitaev-Heisenberg model on a honeycomb lattice
Xiaoyu Dong, D. N. Sheng
Abstract
We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a honeycomb lattice numerically by the infinite density matrix renormalization group method on a cylinder geometry. By tuning the relative value of the Kitaev and Heisenberg exchange couplings, we obtain the phase diagram with two spin liquid phases and four symmetry-broken phases. We identify that the spin liquid phases are gapless by calculating the central charge at the pure Kitaev points without the Heisenberg interactions. Comparing to its spin-1/2 counterpart, the position and number of gapless modes of the spin-1 case are quite different. Due to the approximate ${Z}_{2}$ local conservations, the expectation value of the Wilson loop operator measuring the flux of each plaquette stays near to 1, and the static spin-spin correlations remain short range in the entire spin liquid phases.