Excited State Quantum Phase Transition, Generalized Kibble-Zurek Mechanism, Eigenstate Duality, and Spectrum Structure Duality

Universality and duality are two important concepts in physics. We point out two intriguing dualities for a variety of quantum many-body systems: the eigenstate duality and the spectrum structure duality, with the former between systems of opposite interactions and the latter uncovering an exotic hidden symmetry. Universality class is often discussed in the context of quantum phase transition (QPT) and adiabatic driving dynamics. First, we investigate Excited State Quantum Phase Transition (ESQPT) characterized by a divergent Density of States (DOS) with respect to the energy and parameter variables. This leads to the introduction of two other types of ESQPTs. In the celebrated ground state Kibble-Zurek mechanism (KZM) crossing a second order or continuous phase transition, when the initial ground state is slowly ramped through the continuous QPT critical point, excitations/defects exhibit a power law scaling with respect to the total ramping time τ in the adiabatic limit τ →∞ . We generalize the KZM physics to systems with first-order QPT critical point and find that when the initial state is slowly ramped through a first-order QPT critical point, excitations/defects generated during the slowly driven dynamics also exhibit a power law universal scaling. We further consider the excited state KZ (ESKZ) scenario. For an initial excited eigenstate, the system can be analogously driven slowly through an ESQPT critical point. Excitations/defects generated in the ESKZ scenario can be described by an ESKZM we propose, which predicts also a universal power law scaling in the adiabatic limit τ →∞ . All the cases considered above can be called and described by the generalized KZM (gKZM) which governs the universal behavior for excitations/defects whenever adiabatic dynamics acrossing a QPT critical point happens in a quantum many-body system. We illustrate the related general concepts and mechanism in the model system of a spin-1 atomic Bose-Einstein condensate (BEC).