Designing non-Hermitian real spectra through electrostatics

TL;DR

This paper introduces a novel electrostatics-based method to design non-Hermitian Hamiltonians with real spectra, enabling stable systems without relying on PT symmetry and improving numerical stability for large systems.

Contribution

It develops a comprehensive electrostatics analogy for designing non-Hermitian Hamiltonians with real spectra, bypassing symmetry constraints and enhancing computational efficiency.

Findings

Able to design Hamiltonians with arbitrary spectra and localization profiles

Provides a stable numerical approach for large non-Hermitian systems

Enables reverse-engineering of Hamiltonians without symmetry constraints

Abstract

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 comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra. Our design approach is based on a novel electrostatics analogy for modified non-Hermitian bulk-boundary correspondence, 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 diagonalization of non-Hermitian Hamiltonians as a Poisson boundary value problem, our electrostatics analogy also transcends the gain/loss-induced compounding of floating-point errors in traditional numerical methods, thereby allowing access to far larger system sizes.