  Variational Monte Carlo is a many-body numerical method that scales well with
system size. It has been extended to study the Green function only recently by
Charlebois and Imada (2020). Here we generalize the approach to systems with
open boundary conditions in the absence of translational invariance. Removing
these constraints permits the application of embedding techniques like Cluster
perturbation theory (CPT). This allows us to solve an enduring problem in the
physics of the pseudogap in cuprate high-temperature superconductors, namely
the existence or absence of Fermi arcs in the one-band Hubbard model. We study
the behavior of the Fermi surface and of the density of states as a function of
hole doping for clusters of up to 64 sites, well beyond the reach of modern
exact diagonalization solvers. We observe that the technique reliably captures
the transition from a Mott insulator at half filling to a pseudogap, evidenced
by the formation of Fermi arcs, and finally to a metallic state at large
doping. The ability to treat large clusters with quantum cluster methods helps
to minimize potential finite size effects and enables the study of systems with
long range orders, which will help extend the reach of these already powerful
methods and provide important insights on the nature of various strongly
correlated many-electron systems, including the high-T$_c$ cuprate
superconductors.
