Designing non-Hermitian real spectra through electrostatics

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.

20 pages, 9 figures. v2: corrected typographical errors in parameters and amended references. v3: added additional section to supplement and updated revisions

References in corpus (8)

• Topological Origin of Non-Hermitian Skin Effects
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Zoology of non-Hermitian spectra and their graph topology
• Non-Hermitian Squeezed Polarons
• Filling up complex spectral regions through non-Hermitian disordered chains
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• Anomalous hybridization of spectral winding topology in quantized steady-state responses

Cited by in corpus (28)

• Non-Hermitian Topology and Exceptional-Point Geometries
• Topological Non-Hermitian skin effect
• Dimensional transmutation from non-Hermiticity
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Zoology of non-Hermitian spectra and their graph topology
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Non-Hermitian Squeezed Polarons
• System size dependent topological zero modes in coupled topolectrical chains
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Anomalous fractal scaling in two-dimensional electric networks
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Non-Hermitian spectral flows and Berry-Chern monopoles
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Dynamical suppression of many-body non-Hermitian skin effect in Anyonic systems
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Observation of non-local impedance response in a passive electrical circuit
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• General theory for infernal points in non-Hermitian systems
• Nonlinear Hall effects with an exceptional ring
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Many-body critical non-Hermitian skin effect
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Reversing non-Hermitian skin accumulation with a non-local transverse switch