Algebraic Quantum Spin Liquid from an Exactly Solvable Spin-1/2 Kitaev Model

We propose an exactly solvable quantum spin-1/2 model with time reversal invariance on a two dimensional brick-wall lattice, where each unit cell consists of three sites. We find that the ground states are algebraic quantum spin liquid states. The spinon excitations are gapless and the energy dispersion is linear around two Dirac points. The ground states are of three-fold topological degen-
eracy on a torus. Breaking the time reversal symmetry opens a bulk energy gap and the Z2 vortices obey non-Abelian statistics.