Universal dynamics of the superradiant phase transition in the anisotropic quantum Rabi model

We investigate the universal nonequilibrium dynamics of superradiant phase transition in anisotropic quantum Rabi model. By introducing position and momentum operators, we find generators displaced operators to diagonalize Hamiltonian, then obtain ground states their excitation gaps. According Kibble-Zurek mechanism, that gap near critical point vanishes as $\ensuremath{\omega}\ensuremath{\sim}{|\ensuremath{\epsilon}|}^{\ensuremath{\nu}z}$ with $\ensuremath{\nu}z=1/2$, length scale diverges according $\ensuremath{\zeta}\ensuremath{\sim}{\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\nu}}$, which determines universality class $(z=2,\ensuremath{\nu}=1/4)$ Moreover, by simulating real-time across point, numerically extract exponents from delay ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}_{d}\ensuremath{\sim}{\ensuremath{\tau}}_{Q}^{\ensuremath{-}1/(1+\ensuremath{\nu}z)}$ diverging $\mathrm{\ensuremath{\Delta}}x$, $\mathrm{\ensuremath{\Delta}}p\ensuremath{\sim}{\ensuremath{\tau}}_{Q}^{\ensuremath{\nu}/(1+\ensuremath{\nu}z)}$ (where ${\ensuremath{\tau}}_{Q}$ is quench time). The numerical are well consistent analytical ones. Our study provides a dynamic way explore behaviors