Level statistics of the one-dimensional ionic Hubbard model

TL;DR

This paper investigates how an alternating potential in the one-dimensional ionic Hubbard model shifts its spectral level statistics from integrable Poissonian to chaotic Gaussian ensemble behavior, highlighting the importance of symmetry considerations.

Contribution

It demonstrates that the ionic Hubbard model transitions from integrable to chaotic spectral statistics due to the alternating potential, emphasizing the role of symmetry block analysis.

Findings

Without alternating potential, the model exhibits Poissonian statistics.

With alternating potential, spectral properties resemble Gaussian ensemble statistics.

Symmetry block analysis is essential to observe this transition.

Abstract

In this work we analyze the spectral level statistics of the one-dimensional ionic Hubbard model, the Hubbard model with an alternating on-site potential. In particular, we focus on the statistics of the gap ratios between consecutive energy levels. This quantity is often used in order to signal whether a many-body system is integrable or chaotic. A chaotic system has typically the statistics of a Gaussian ensemble of random matrices while the spectral properties of the integrable system follow a Poisson statistics. We find that whereas the Hubbard model without alternating potential is known to be integrable and its spectral properties follow a Poissonian statistics, the presence of an alternating potential causes a drastic change in the spectral properties which resemble the one of a Gaussian ensemble of random matrices. However, to uncover this behavior one has to separately consider the blocks of all symmetries of the ionic Hubbard model.