Discriminant indicators with generalized inversion symmetry

We propose indicators of the discriminant for systems with generalized inversion symmetry which are computed from data only at high-symmetry points in the Brillouin zone. Our approach captures the exceptional points and their symmetry-protected variants without ambiguity arising from the reference energy, which is advantage over the previously known indicators for non-Hermitian systems. As demonstrations, we systematically analyze $3\times 3$-Hamiltonians where the proper choice of the reference energy is not obvious.