Peratic phase transition by bulk-to-surface response

The study of dynamical phase transitions has been attracting considerable research efforts in the last decade. One theme of present interest is to search for exotic scenarios beyond the framework of equilibrium phase transitions. Here, we establish a duality between many-body dynamics and static Hamiltonian ground states for both classical and quantum systems. We construct frustration-free Hamiltonians whose ground-state phase transitions have rigorous duality to chaotic transitions in dynamical systems. By this duality, we show that the corresponding ground-state phase transitions are characterized by a bulk-to-surface response; these phase transitions are then dubbed “peratic,” meaning that they are defined by their response to the boundary. For the classical system, we show how the timelike dimension emerges in the static ground states. For the quantum system, the ground state is a superposition of geometrical lines on a two-dimensional array; these lines encode the dynamical Floquet evolution history of one-dimensional disordered spin chains. Our prediction of a peratic phase transition has direct consequences in quantum simulation platforms such as Rydberg atoms and superconducting qubits, as well as anisotropic spin glass materials. The discovery would shed light on the unification of dynamical phase transitions with equilibrium systems.