Interrelated Thermalization and Quantum Criticality in a Lattice Gauge Simulator

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.