Exceptional points near first- and second-order quantum phase transitions

We study impact of quantum phase transitions (QPTs) on the distribution of exceptional points (EPs) of the Hamiltonian in complex-extended parameter domain. Analyzing first- and second-order QPTs in the Lipkin model, we find an exponentially and polynomially close approach of EPs to the respective critical point with an increasing size of the system. If the critical Hamiltonian is subject to random perturbations of various kinds, the averaged distribution of EPs close to the critical point still carries decisive information on the QPT type. We therefore claim that properties of the EP distribution represent a parametrization-independent signature of criticality in quantum systems.