The operator known as entanglement (or modular) Hamiltonian encodes the information of entanglement in a given quantum state. We compute this entanglement Hamiltonian in states (density matrices obtained by bi-partitioning a Cauchy slice), which are obtained by perturbing a field theory vacuum by a unitary. We show that the type-III nature of the field theory von-Neumann operator algebra is manifested through an end-point contribution arising out of the entangling surface separating the two subregions. Several applications and implications follow. Based on work in progress with Dan Kabat, Aakash Marthandan and Xiaole Jiang, and a couple of prior works.
