I'm trying to better understand which kinds of interactions cause the entanglement.
I do understand how it works in the cases of non-relativistic spin systems. For example, evolving a pure state in time with the Hamiltonian of the form $\vec{\sigma}^{(j)} \cdot \vec{\sigma}^{(j+1)}$ will likely result in an entangled state.
What about the following physical systems:
- Non-relativistic QM of a finite number of particles with a Hamiltonian having only coordinate dependence (no spins).
- Same as 1., but with only spin-spin and coordinate-coordinate interactions (nothing like spin-orbital interaction).
- Relativistic field theory describing interactions of fields with zero/nonero spin. Importantly, such a theory is manifestly local.
Which terms in these cases cause entanglement during the time evolution?
I would also expect that this question may be related to another one:
What are the conditions on the Hamiltonian for its eigenstates (or, at least, the ground state) to be unentangled?
