Model for frustrated spin-orbital chains as applied to CaV2 O4

Motivated by recent interest in quasi-one-dimensional compound CaV2 O4, 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 the Jahn-Teller effect compete with intersite 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 CaV2 O4 are discussed.