Scaling behavior and phase diagram of a PTPT-symmetric non-Hermitian Bose–Hubbard system

We study scaling behavior and phase diagram of a PTPT-symmetric non-Hermitian Bose–Hubbard model. In the free interaction case, using both analytical and numerical approaches, the metric operator for many-particle is constructed. The derived properties of the metric operator, similarity matrix and equivalent Hamiltonian reflect the fact that all the matrix elements change dramatically with diverging derivatives near the exceptional point. In the nonzero interaction case, it is found that even small on-site interaction can break the PTPT symmetry drastically. It is demonstrated that the scaling law can be established for the exceptional point in both small and large interaction limit. Based on perturbation and numerical methods, we also find that the phase diagram shows rich structure: there exist multiple regions of unbroken PTPT symmetry.

► Generalization is done to many-particle sector of PT-symmetric non-Hermitian system.
► The metric operator, similarity matrix and equivalent Hamiltonian possess diverging derivatives near the exceptional point.
► The scaling law is established for the exceptional point of a PT-symmetric non-Hermitian Bose–Hubbard model.
► The phase diagram shows that multiple regions of unbroken PT symmetry exist.
► It is shown that even small on-site interaction can break the PT symmetry drastically.