Finding Short-Range Parity-Time Phase-Transition Points with a Neural Network

The non-Hermitian PT-symmetric system can live in either unbroken or broken PT-symmetric phase. The separation point of the unbroken and broken PT-symmetric phases is called the PT-phase-transition point. Conventionally, given an arbitrary non-Hermitian PT-symmetric Hamiltonian, one has to solve the corresponding Schrödinger equation explicitly in order to determine which phase it is actually in. Here, we propose to use artificial neural network (ANN) to determine the PT-phase-transition points for non-Hermitian PT-symmetric systems with short-range potentials. The numerical results given by ANN agree well with the literature, which shows the reliability of our new method.