  We consider the Rabi Hamiltonian which exhibits a quantum phase transition
(QPT) despite consisting only of a single-mode cavity field and a two-level
atom. We prove QPT by deriving an exact solution in the limit where the atomic
transition frequency in unit of the cavity frequency tends to infinity. The
effect of a finite transition frequency is studied by analytically calculating
finite-frequency scaling exponents as well as performing a numerically exact
diagonalization. Going beyond this equilibrium QPT setting, we prove that the
dynamics under slow quenches in the vicinity of the critical point is
universal, that is, the dynamics is completely characterized by critical
exponents. Our analysis demonstrates that the Kibble-Zurek mechanism can
precisely predict the universal scaling of residual energy for a model without
spatial degrees of freedom. Moreover, we find that the onset of the universal
dynamics can be observed even with a finite transition frequency.
