  Strongly interacting electrons in layered materials give rise to a plethora
of emergent phenomena, such as unconventional superconductivity. heavy
fermions, and spin textures with non-trivial topology. Similar effects can also
be observed in bulk materials, but the advantage of two dimensional (2D)
systems is the combination of local accessibility by microscopic techniques and
tuneability. In stacks of 2D materials, for example, the twist angle can be
employed to tune their properties. However, while material choice and twist
angle are global parameters, the full complexity and potential of such
correlated 2D electronic lattices will only reveal itself when tuning their
parameters becomes possible on the level of individual lattice sites. Here, we
discover a lattice of strongly correlated electrons in a perfectly ordered 2D
supramolecular network by driving this system through a cascade of quantum
phase transitions using a movable atomically sharp electrostatic gate. As the
gate field is increased, the molecular building blocks change from a
Kondo-screened to a paramagnetic phase one-by-one, enabling us to reconstruct
their complex interactions in detail. We anticipate that the supramolecular
nature of the system will in future allow to engineer quantum correlations in
arbitrary patterned structures.
