  We use non-equilibrium dynamical mean-field theory with iterative
perturbation theory as an impurity solver to study the recovery of $SU(2)$
symmetry in real-time following a hopping integral parameter quench from a
mass-imbalanced to a mass-balanced single-band Hubbard model at half-filling. A
dynamical order parameter $\gamma(t)$ is defined to characterize the evolution
of the system towards $SU(2)$ symmetry. By comparing the momentum dependent
occupation from an equilibrium calculation (with the $SU(2)$ symmetric
Hamiltonian after the quench at an effective temperature) with the data from
our non-equilibrium calculation, we conclude that the $SU(2)$ symmetry
recovered state is a thermalized state. Further evidence from the evolution of
the density of states supports this conclusion. At the same time, we find the
order parameter in the weak Coulomb interaction regime undergoes an approximate
exponential decay. We numerically investigate the interplay of the relevant
parameters (initial temperature, Coulomb interaction strength, initial
mass-imbalance ratio) and their combined effect on the thermalization behavior.
Finally, we study evolution of the order parameter as the hopping parameter is
changed with either a linear ramp or a pulse. Our results can be useful in
strategies to engineer the relaxation behavior of interacting, quantum
many-particle systems.
