Fractionalization, entanglement, and separation: Understanding the collective excitations in a spin-orbital chain

Using a combined analytical and numerical approach, we study the collective spin and orbital excitations in a spin-orbital chain under a crystal field. Irrespective of the crystal field strength, these excitations can be universally described by fractionalized resonating-valence-bond fermions. Each of the fractional quasiparticles carries both spin and orbital quantum numbers, and thereby the spin and orbital variables are always entangled in the collective excitations. The result shows that the recently reported spin-orbital separation occurs solely due to a particular choice of basis, which is valid only when crystal fields fully polarize the orbital degrees of freedom. The persistent fractionalization contrasts strikingly with the case of a spin chain, where fractionalized spinons cannot be individually observed but confined to form magnons of integral quantum numbers in a strong magnetic field.