  Studying strong electron correlations has been an essential driving force for
pushing the frontiers of condensed matter physics. In particular, in the
vicinity of correlation-driven quantum phase transitions (QPTs), quantum
critical fluctuations of multiple degrees of freedom facilitate exotic
many-body states and quantum critical behaviors beyond Landau's framework.
Recently, moir\'e heterostructures of van der Waals materials have been
demonstrated as a highly tunable quantum platform for exploring fascinating
strongly correlated quantum physics. Here, we report the observation of tunable
quantum criticalities in an experimental simulator of extended Hubbard model
with spin-valley isospins arising in chiral-stacked twisted double bilayer
graphene. Scaling analysis shows a quantum two-stage criticality manifesting
two distinct quantum critical points as the generalized Wigner crystal transits
to a Fermi liquid by varying the displacement field, suggesting the emergence
of a critical intermediate phase. The quantum two-stage criticality evolves
into a quantum pseudo criticality as a high parallel magnetic field is applied.
In such pseudo criticality, we find that the quantum critical scaling is only
valid above a critical temperature, indicating a weak first-order QPT therein.
Our results demonstrate a highly tunable solid-state simulator with intricate
interplay of multiple degrees of freedom for exploring exotic quantum critical
states and behaviors.
