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Universal Thouless relations for disordered non-Hermitian systems in one dimension.
1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
Science Bulletin
|June 12, 2026
Summary
Researchers developed universal Thouless relations (UTRs) for disordered non-Hermitian systems. These relations quantitatively predict spectral densities and localization, revealing a topological transition between skin and Anderson localization regimes.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Topological physics
Background:
- Disordered non-Hermitian systems display unique localization phenomena not seen in Hermitian systems.
- A quantitative framework for understanding their spectra and localization has been absent.
- Existing methods often require computationally intensive large-scale diagonalizations.
Purpose of the Study:
- To establish a unified and quantitative framework for spectra and localization in one-dimensional disordered non-Hermitian systems.
- To introduce universal Thouless relations (UTRs) applicable to various system parameters.
- To elucidate the nature of the transition between skin and Anderson localization regimes.
Main Methods:
- Derivation of universal Thouless relations (UTRs) connecting spectral densities and Lyapunov exponents.
- Application of UTRs to determine spectral properties and localization in the thermodynamic limit.
- Analysis of the topological nature of the skin-Anderson transition by examining Lyapunov gaps.
Main Results:
- UTRs are established, applicable to arbitrary hopping and disorder, enabling prediction without diagonalization.
- The transition between skin and Anderson regimes is identified as topological, driven by a closing Lyapunov gap.
- A novel unidirectional multifractal state is discovered at the transition point.
- An exact topological criterion is derived to distinguish localization regimes.
Conclusions:
- The UTRs provide a unified framework for studying disordered non-Hermitian systems.
- The findings offer new methods for predicting and controlling wave localization phenomena.
- The topological nature of localization transitions is highlighted, opening new research avenues.
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