Entanglement Hamiltonians for Chiral Fermions with Zero Modes

In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in $(1+1)\mathrm{D}$. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy.

Figure 1

The entanglement region $V=\cup (a_{j,}{b}_j)$ for fermions on a ring of radius $R$ considered in the Letter, and an associated Riemann-Hilbert problem.