  We provide a framework for understanding the gapless Kitaev spin liquid (KSL)
in the language of tensor network(TN). Without introducing Majorana fermion,
most of the features of the KSL including the symmetries, gauge structure,
criticality and vortex-freeness are explained in a compact TN representation.
Our construction reveals a hidden string gas structure of the KSL. With only
two variational parameters to adjust, we obtain an accurate KSL ansatz with the
bond dimension D = 8 in a compact form, where the energy is about 0.007% higher
than the exact one. In addition, the opening of gap and non-Abelian phase
driven by a magnetic field are naturally understood in our construction.
