Figure 1

Schematic comparison of conventional and dynamical quantum phase transitions. (a) Equilibrium temperature—control parameter phase diagram. A quantum phase transition (QPT) is a continuous phase transition occurring at T = 0 and separating two phases, e.g., a ferromagnet for g < g c from a paramagnet for g > g c (black arrows). At g c , physical quantities become nonanalytic upon varying g (yellow arrows), triggered by a change in the spectrum of the system Hamiltonian H = H 0 + H 1 ( g ) , which becomes gapless as indicated by the schematic energy-level structure. Though only occurring at T = 0 , QPTs control the system’s properties also in the quantum critical region at T > 0 . (b) Dynamics in the energy density—time plane. A DQPT occurs along the ϵ = 0 axis at t = t c , separating two regimes of, e.g., opposite magnetization (black arrows). The DQPT is not associated with a change in the spectrum but with an incisive redistribution of occupations between the eigenstates of the initial Hamiltonian H 0 , induced by the perturbation H 1 . In the present experiment, H 0 exhibits two degenerate ground states of opposite magnetization, and the DQPT is caused by a sudden change of the low-energy occupations from one of the two ground states to the other. Though the mean energy density (red line), where many observables acquire their dominant contribution, lies at ϵ > 0 , the nonequilibrium dynamics of observables can still be controlled by the underlying DQPT (white space).