Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian

TL;DR

This paper compares level statistics in various quantum many-body models, showing GOE behavior in generic cases and Poisson statistics at integrable points, confirming theoretical predictions.

Contribution

It demonstrates the transition from GOE to Poisson statistics at integrable points across multiple models, providing empirical validation.

Findings

GOE statistics dominate in generic models

Poisson statistics appear at integrable points

Results align with theoretical expectations

Abstract

We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at points corresponding to models known to be exactly integrable Poisson statistics are found, in agreement with an argument we outline.