# Extended states with Poisson spectral statistics

## TL;DR

This paper demonstrates that extended states in certain complex systems can exhibit Poisson spectral statistics under specific constraints, challenging common assumptions and advancing understanding of eigenfunction localization.

## Contribution

It introduces a novel class of constrained chiral ensembles with circulant off-diagonal blocks, showing their spectral properties and relevance to physical localization phenomena.

## Key findings

- Extended states can have Poisson spectral statistics under specific constraints.
- Exact theoretical and numerical analysis confirms the spectral behavior.
- Results impact understanding of eigenfunction localization in complex systems.

## Abstract

Contrary to prevailing notion we find that the spectrum associated with the extended states in a complex system may belong to the Poisson universality class if the system is subjected to a specific set of constraints. Our results are based on an exact theoretical as well as numerical analysis of column constrained chiral ensembles with circulant off-diagonal blocks and are relevant for a complete understanding of the eigenfunction localization and related physical properties.