Recently, more and more non-Hermitian systems are experimentally simulated in many optical set up with gain and loss. Besides the optics, the condensed matter theorists have been recently studying on the non-Hermitian effect in the PT-symmetric systems, e.g. the non-Hermitian Su-Schriffer-Heeger (SSH) model. The exceptional point (EP) of a non-Hermitian Hamiltonian is particularly interesting to be analysed before playing with the non-Hermitian systems. However, due to the non-Hermitian quantum mechanics is still new for many researchers, the lack of theoretical tools to detect EP has become a top priority. In our work, the fidelity susceptibility is generalized to the non-Hermitian system by including the geometry of the Hilbert space. The fidelity susceptibility is originally used for detecting quantum phase transition. Now we find that it is also a good tool for the EP.

Reference arXiv:2009.07070