Level statistics of the one-dimensional dimerized Hubbard model

TL;DR

This paper studies the level statistics of a one-dimensional dimerized Hubbard model, revealing that its spectral properties align with predictions from random matrix theory when symmetries are properly accounted for.

Contribution

It demonstrates that, after symmetry considerations, the level spacings of the model follow Gaussian orthogonal ensemble distributions, providing insights into the system's quantum chaos.

Findings

Level spacings follow GOE distribution after symmetry reduction

Distribution of ratios of consecutive level spacings matches RMT predictions

Quantitative measures show deviations are minimal in large systems

Abstract

The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi-Hubbard model with dimerized hopping amplitude and find that after taking into account translation, reflection, spin and {\eta} pairing symmetries to isolate irreducible blocks of the Hamiltonian, the level spacings in the limit of large system sizes follow the distribution expected for hermitian random matrices from the Gaussian orthogonal ensemble. We show this by analyzing the distribution of the ratios of consecutive level spacings in this system, its cumulative distribution and quantify the deviations of the distributions using their mean, standard deviation and skewness.