  Quantum spin-orbital liquids (QSOLs) are a novel phase of matter, similar to
quantum spin liquids, with quantum fluctuations in both spin and orbital
degrees of freedom. We use non-equilibrium Green's function theory to study
out-of-equilibrium spin transport in an exactly solvable QSOL model put forward
by Yao and Lee. We find that the spin transport problem can be mapped to that
of a free fermion problem with effective fermionic baths that have rapidly
varying density of states. In the gapless phase, the spin current $I_s-V_s$
relation is thus highly nonlinear, while in the chiral gapped phase, the spin
current conductance is quantized to be $1/2\pi$ provided that the contacts are
sufficiently wide. The quantized conductance is a signature of the topological
nature of the chiral gapped QSOL.
