Peratic Phase Transition by Bulk-to-Surface Response

TL;DR

This paper introduces 'peratic' phase transitions characterized by bulk-to-surface responses, establishing a duality between dynamical chaos and static ground states in classical and quantum systems, with implications for quantum simulation.

Contribution

It establishes a duality linking dynamical chaos to static ground state phase transitions and introduces the concept of peratic phase transitions characterized by boundary responses.

Findings

Ground state phase transitions are dual to chaotic dynamical transitions.

Peratic phase transitions are characterized by bulk-to-surface boundary responses.

Predictions applicable to quantum simulators and spin glass materials.

Abstract

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 the corresponding ground state phase transitions are characterized by bulk-to-surface response, which are then dubbed "peratic" meaning defined by response to the boundary. For the classical system, we show how the time-like 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, which encode the dynamical Floquet evolution history of one dimensional disordered spin chains. Our prediction of 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.