  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.
