  Motivated by recent interest in quasi-one-dimensional compound CaV2O4, we
study the ground states of a spin-orbital chain characterized by an Ising-like
orbital Hamiltonian and frustrated interactions between S=1 spins. The on-site
spin-orbit interaction and Jahn-Teller effect compete with inter-site
superexchange leading to a rich phase diagram in which an antiferro-orbital
phase is separated from the orbital paramagnet by a continuous Ising
transition. Two distinct spin liquids depending on the underlying orbital order
are found in the limit of small spin-orbit coupling. In the opposite limit, the
zigzag chain behaves as a spin-2 chain with Ising anisotropy. The implications
for CaV2O4 are discussed.
