Entanglement Hamiltonians for Periodic Free Fermion Chains with Defects

We study the half system entanglement Hamiltonians of the ground state of free fermion critical transverse field Ising model with periodic boundary conditions in the presence of defects. In general, we observe that these defects introduce non-local terms into the entanglement Hamiltonian, with the most significant being couplings across the defect that decay with distance. We also perform a limited entanglement Hamiltonian reconstruction using an ansatz and analyze how the fitted non-local couplings vary with defect strength.