  It is still debated whether the low-doping Fermi surface of cuprates is
composed of hole pockets or of disconnected Fermi arcs. Results from cellular
dynamical mean field theory (c-DMFT) support the Fermi arcs hypothesis by
predicting corresponding Fermi arcs for the Hubbard model. Here, we introduce a
simple parametrization of the self-energy, in the spirit of Yang-Rice-Zhang
theory, and show that state of the art c-CDMFT calculations cannot give a
definitive answer to the question of Fermi arcs vs holes pockets, and this,
independently of the periodization (cumulant or Green's function) used to
display spectral weights of the infinite lattice. Indeed, when our model is
restricted to a cluster and periodized like in c-DMFT, only two adjustable
parameters suffice to reproduce the qualitative details of the frequency and
momentum dependence of the low energy c-DMFT spectral weight for both
periodizations. In other words, even though our starting model has a Fermi
surface composed of hole and electron pockets, it leads to Fermi arcs when
restricted to a cluster and periodized like in c-DMFT. We provide a new
"compact tiling" scheme to recover the hole and electron pockets of our
starting non-interacting lattice model, suggesting that better periodization
schemes might exist.
