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Designing non-hermitian real spectra through electrostatics

Yang, Russell and Tan, Jun Wei and Tai, Tommy and Koh, Jin Ming and Li, Linhu and Longhi, Stefano and Lee, Ching Hua (2022) Designing non-hermitian real spectra through electrostatics. Science Bulletin, 67 (18). pp. 1865-1873. ISSN 2095-9273. doi:10.1016/j.scib.2022.08.005.

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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 new 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 oating-point errors in traditional numerical methods, thereby allowing access to far larger system sizes.

Item Type:Article
Related URLs:
URLURL TypeDescription
Tai, Tommy0000-0002-9478-5499
Koh, Jin Ming0000-0002-6130-5591
Lee, Ching Hua0000-0003-0690-3238
Additional Information:© 2022 Elsevier. Received 12 March 2022, Revised 29 June 2022, Accepted 29 July 2022, Available online 6 August 2022. This work is supported by Singapore’s MOE Tier I grant WBS no. A-800022-00-00. AUTHOR CONTRIBUTIONS. Ching Hua Lee developed the electrostatics analogy and initiated the project. Ching Hua Lee and Russell Yang led the project. Jun Wei Tan performed the spectral reconstruction. Russell Yang, Jun Wei Tan, Tommy Tai, and Jin Ming Koh performed the numerical computations. Stefano Longhi generalized the electrostatics analogy to point charges. Stefano Longhi, Linhu Li, and Ching Hua Lee also took on advisory roles. All authors contributed to the writing of the manuscript. The authors declare that they have no conflict of interest.
Funding AgencyGrant Number
Ministry of Education (Singapore)A-800022-00-00
Subject Keywords:Non-hermitian; Electrostatics; Bulk-boundary correspondence; Band structure engineering; Real spectrum; Non-Hermitian Skin effect
Issue or Number:18
Record Number:CaltechAUTHORS:20220808-223906000
Persistent URL:
Official Citation:Russell Yang, Jun Wei Tan, Tommy Tai, Jin Ming Koh, Linhu Li, Stefano Longhi, Ching Hua Lee, Designing non-hermitian real spectra through electrostatics, Science Bulletin, 2022, , ISSN 2095-9273,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116164
Deposited By: George Porter
Deposited On:09 Aug 2022 20:48
Last Modified:18 Nov 2022 00:40

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