Bootstrapping non-Hermitian quantum systems

Recently, the “bootstrap” technique was applied in quantum mechanics to solve the eigenspectra of Hermitian Hamiltonians and extended to non-Hermitian parity-time (PT)-symmetric systems. However, its application has been limited to real spectra. In this work, we establish bootstrap conditions for the non-Hermitian system and generate eigenspectra for a generic complex polynomial potential, which includes PT-symmetric Hamiltonians as a special case. Additionally, we demonstrate the method’s ability to obtain eigenspectra under various boundary conditions imposed on the eigenfunction, including the notable application of capturing the PT-symmetric phase transition.