  Interacting fermions on a lattice can develop strong quantum correlations,
which lie at the heart of the classical intractability of many exotic phases of
matter. Seminal efforts are underway in the control of artificial quantum
systems, that can be made to emulate the underlying Fermi-Hubbard models.
Electrostatically confined conduction band electrons define interacting quantum
coherent spin and charge degrees of freedom that allow all-electrical
pure-state initialisation and readily adhere to an engineerable Fermi-Hubbard
Hamiltonian. Until now, however, the substantial electrostatic disorder
inherent to solid state has made attempts at emulating Fermi-Hubbard physics on
solid-state platforms few and far between. Here, we show that for gate-defined
quantum dots, this disorder can be suppressed in a controlled manner. Novel
insights and a newly developed semi-automated and scalable toolbox allow us to
homogeneously and independently dial in the electron filling and
nearest-neighbour tunnel coupling. Bringing these ideas and tools to fruition,
we realize the first detailed characterization of the collective Coulomb
blockade transition, which is the finite-size analogue of the
interaction-driven Mott metal-to-insulator transition. As automation and device
fabrication of semiconductor quantum dots continue to improve, the ideas
presented here show how quantum dots can be used to investigate the physics of
ever more complex many-body states.
