Low energy transition in spectral statistics of 2D interactingfermions

TL;DR

This paper investigates how Coulomb interactions induce a transition from localized to ergodic behavior in 2D spinless fermions, revealing a universal energy-driven transition in spectral statistics.

Contribution

It demonstrates a disorder-independent transition in spectral statistics from Poisson to Wigner-Dyson, indicating interaction-induced quantum ergodicity in 2D fermionic systems.

Findings

Transition from Poisson to Wigner-Dyson distribution at a critical energy

Transition is independent of the number of fermions

Indicates interaction-driven delocalization and ergodicity

Abstract

We study the level spacing statistics $P(s)$ and eigenstate properties of spinless fermions with Coulomb interaction on a two dimensional lattice at constant filling factor and various disorder strength. In the limit of large lattice size, $P(s)$ undergoes a transition from the Poisson to the Wigner-Dyson distribution at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature.