Designing non-Hermitian real spectra through electrostatics

Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in designing them through enforcing parity-time (PT) symmetry. In this work, we exploit a lesser-known dynamical mechanism for enforcing real-spectra, and develop a comprehen-sive and versatile approach for designing new classes of parent Hamiltonians with real spectra. Our design approach is based on a new electrostatics analogy for modified non-Hermitian bulk-boundary cor-respondence, where electrostatic charge corresponds to density of states and electric fields correspond to complex spectral flow. As such, Hamiltonians of any desired spectra and state localization profile can be reverse-engineered, particularly those without any guiding symmetry principles. By recasting the diago-nalization of non-Hermitian Hamiltonians as a Poisson boundary value problem, our electrostatics anal-ogy also transcends the gain/loss-induced compounding of floating-point errors in traditional numerical methods, thereby allowing access to far larger system sizes.