Parity-time symmetry under magnetic flux

We study a parity-time (PT) symmetric ring lattice, with one pair of balanced gain and loss located at opposite positions. The system remains PT-symmetric when threaded by a magnetic flux; however, the PT symmetry is sensitive to the magnetic flux, in the presence of a large balanced gain and loss, or in a large system. We find a threshold gain/loss, above which, any nontrivial magnetic flux breaks the PT symmetry. We obtain the maximally tolerable magnetic flux for the exact PT-symmetric phase, which is approximately linearly dependent on a weak gain/loss.