  Quantum critical behavior of many-body phase transitions is one of the most
fascinating yet challenging questions in quantum physics. Here, we improved the
band-mapping method to investigate the quantum phase transition from superfluid
to Mott insulators, and we observed the critical behaviors of quantum phase
transitions in both dynamical steady-state-relaxation region and
phase-oscillation region. Based on various observables, two different values
for the same quantum critical parameter are observed. This result is beyond a
universal-scaling-law description of quantum phase transitions known as the
Kibble-Zurek mechanism, and suggests that multiple quantum critical mechanisms
are competing in many-body quantum phase transition experiments in
inhomogeneous systems.
