Modular Hamiltonians for the massless Dirac field in the presence of a defect

Understand

We study the massless Dirac field on the line in the presence of a point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission.

• Considering this system in its ground state, we derive the modular Hamiltonians of the subregion given by the union of two disjoint equal intervals at the same distance from the defect.
• The absence of energy dissipation at the defect implies the existence of two phases, where either the vector or the axial symmetry is preserved.
• Besides a local term, the densities of the modular Hamiltonians contain also a sum of scattering dependent bi-local terms, which involve two conjugate points generated by the reflection and the transmission.