  Gauge theory and thermalization are both foundations of physics and nowadays
are both topics of essential importance for modern quantum science and
technology. Simulating lattice gauge theories (LGTs) realized recently with
ultracold atoms provides a unique opportunity for carrying out a correlated
study of gauge theory and thermalization in the same setting. Theoretical
studies have shown that an Ising quantum phase transition exists in this
implemented LGT, and quantum thermalization can also signal this phase
transition. Nevertheless, it remains an experimental challenge to accurately
determine the critical point and controllably explore the thermalization
dynamics in the quantum critical regime due to the lack of techniques for
locally manipulating and detecting matter and gauge fields. Here, we report an
experimental investigation of the quantum criticality in the LGT from both
equilibrium and non-equilibrium thermalization perspectives by equipping the
single-site addressing and atom-number-resolved detection into our LGT
simulator. We accurately determine the quantum critical point agreed with the
predicted value. We prepare a $|Z_{2}\rangle$ state deterministically and study
its thermalization dynamics across the critical point, leading to the
observation that this $|Z_{2}\rangle$ state thermalizes only in the critical
regime. This result manifests the interplay between quantum many-body scars,
quantum criticality, and symmetry breaking.
