Entanglement entropy in the Ising conformal field theory with topological defects

Entanglement entropy (EE) in conformal field theories (CFTs) contains signatures of the universal characteristics of the CFTs. The existence of boundaries and defects in the CFT leads to universal contributions to the EE which can be used to identify these features of the theory. In this work, we investigate EE of a subsystem in the Ising CFT in the presence of a topological defect. The latter is the purely transmitive case of the more general conformal defect and is deeply related to the internal symmetries of the CFT. We demonstrate that the behavior of the EE depends crucially on geometric arrangement of the subsystem with respect to the defect, in particular, whether the defect lies within the subsystem or precisely at the edge of the subsystem, with rather unexpected results for the latter case. We show that the topological defect necessarily comes in conjunction with zero-energy modes. We quantify the nontrivial subleading contributions to the EE arising due to these zero-modes when the subsystem size is a finite fraction of the total system size. We perform these computations starting from an appropriate lattice model and mapping the defect Hamiltonian to a free-fermion model using Jordan-Wigner transformation.