Non-Hermitian fractional quantum Hall states with 1/3 filling*

We elucidate the emergence of non-Hermitian fractional quantum Hall states (nHFQH) with 1/3 filling for cold atoms with two-body loss. We characterize the nHFQH states with the topological degeneracy under the periodic boundary condition and the total Chern number Ctot=1 for the ground state triplet. Furthermore, we point out that nHFQH states emerge even when the interaction is purely dissipative.