Symmetry protected exceptional points of interacting fermions

Non-Hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a nondiagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in noninteracting systems. Here we investigate the fate of such symmetry protected exceptional points in the presence of a symmetry preserving interaction between fermions and find that (i) exceptional points are stable in the presence of the interaction. Their propagation through the parameter space leads to the formation of characteristic exceptional “fans.” In addition, (ii) we identify a new source for exceptional points which are only present due to the interaction. These points emerge from diagonalizable degeneracies in the noninteracting case. Beyond their creation and stability, (iii) we also find that exceptional points can annihilate each other if they meet in parameter space with compatible many-body states forming a third order exceptional point at the endpoint. These phenomena are well captured by an “exceptional perturbation theory” starting from a noninteracting Hamiltonian.