On the relation between entanglement and subsystem Hamiltonians
  We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling range differs in both quantities and allow to investigate the effect. 
Ingo Peschel and Ming-Chiang Chung
cond-mat.stat-mech