Exceptional-point-induced dynamic sensitivity to particle-number parity

As an exclusive feature of a non-Hermitian system, the existence of exceptional points (EPs) depends not only on the details of the Hamiltonian but also on the particle-number filling and the particle statistics. In this paper, we study many-particle EPs in a Bose Hubbard chain with two end-site resonant imaginary potentials. Starting from a single-particle coalescing eigenstate, we construct $n$-particle condensate eigenstates for the cases with zero and infinite $U$. Compared with the free bosonic case, where the $n$-particle condensate eigenstate is an $(n+1)$-th-order coalescing state, the hardcore-boson counterpart is a second-order coalescing state for odd $n$ , while it is not for even $n$. The difference in particle-number parity results in distinct quenching dynamics of the condensate states, highlighting the role of parity in system behavior. Our finding may stimulate research on the dynamic sensitivity to particle-number parity.