Finding Short-Range Parity-Time Phase-Transition Points with a Neural NetworkSupported by the National Natural Science Foundation of China (Grant Nos. 11535004, 11975167, 11761161001, 11375086, 11565010, 11881240623 and 11961141003), the National Key R&D Program of China (Grant Nos. 2018YFA0404403 and 2016YFE0129300), the Science and Technology Development Fund of Macau (Grant No. 008/2017/AFJ), and the Fundamental Research Funds for the Central Universities (Grant

Abstract

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.