Enlarged non-Hermitian Su-Schrieffer-Heeger Model with Broken Locality

In this talk, we embedded the non-Hermitian Su-Schrieffer-Heeger (SSH) model on a hermitian model by Naimark dilation, which attaching an ancilla. We find that a long range hopping term occurs in such enlarged hermitian Hamiltonian. Although such enlargement preserve the spectrum and the relativistic dispersion, the entanglement entropy evaluated from the eigenstate does not follow the Cardy-Calabrese formalism, which is caused by the the long range hopping term, resulting the breaking of locality.