  Taking the quantum Kitaev chain as an example, we have studied the universal
dynamical behaviors resulting from quantum criticality under the condition of
environmental temperature quench. Our findings reveal that when the quantum
parameter is at its critical value, both the excess excitation density at the
end of linear quench and the subsequent free relaxation behavior exhibit
universal scaling behaviors. The scaling laws observed upon quenching to the
zero-temperature quantum critical point and non-zero temperature points exhibit
distinct scaling exponents, which are all intimately related to the dynamical
critical exponents of the quantum phase transition. Additionally, for the case
of linear quench to finite temperatures, we have also discovered an intrinsic
universal dynamical behavior that is independent of quantum criticality. Our
research offers profound insights into the relationship between quantum
criticality and nonequilibrium dynamics from two perspectives:
Kibble-Zurek-like scaling behavior and free relaxation dynamics. Notably, the
Kibble-Zurek-like scaling behavior in this context differs from the standard
Kibble-Zurek mechanism. These two aspects jointly open up a new avenue for us
to understand quantum criticality through real-time dynamical behavior, even at
finite temperatures.
