# Non-ergodic extended states in the SYK model

## TL;DR

This paper analytically investigates the SYK model with a one-body perturbation, revealing a regime where spectral correlations are chaotic but wave functions are non-ergodic and fractal, indicating a new phase of quantum behavior.

## Contribution

It identifies a broad intermediate coupling regime in the SYK model where spectral statistics are chaotic but wave functions are non-ergodic and fractal, a novel phase in strongly interacting systems.

## Key findings

- Spectral correlations follow Wigner-Dyson statistics.
- Wave functions exhibit fractal, non-uniform distribution.
- Non-ergodic extended states are prevalent in this regime.

## Abstract

We analytically study spectral correlations and many body wave functions of an SYK-model deformed by a one body contribution to the Hamiltonian. Our main result is the identification of a wide range of intermediate coupling strengths where the spectral statistics is of Wigner-Dyson type, while wave functions are non-uniformly distributed over Fock space and show fractal behavior. The structure of the theory suggests that such manifestations of non-ergodic extendedness may be a prevalent phenomenon in strongly interacting chaotic quantum systems.