  We introduce a spin-orbital entangled (SOE) resonating valence bond (RVB)
state on a square lattice of spins-$\frac12$ and orbitals represented by
pseudospins-$\frac12$. Like the standard RVB state, it is a superposition of
nearest-neighbor hard-core coverings of the lattice by spin singlets, but
adjacent singlets are favoured to have perpendicular orientations and, more
importantly, an orientation of each singlet is entangled with orbitals' state
on its two lattice sites. The SOE-RVB state can be represented by a projected
entangled pair state (PEPS) with a bond dimension $D=4$. This representation
helps to reveal that the state is a superposition of striped coverings
conserving a topological quantum number. The stripes are a critical quantum
spin liquid. We propose a spin-orbital Hamiltonian supporting a SOE-RVB ground
state.
