Entanglement entropy of heterogenous system

We calculate the entanglement entropy (EE) between two coupled heterogenous spin chains. The two subsystems could be respectively gapped, conformal critical and Lifshitz critical. In regard of how EE scales with the system length, we investigate when logarithmic law or area law is obeyed. Furthermore, sub-leading term of area law is studied, through which, Lifshitz subsystems distinguish themselves.