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Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging Different Concepts of Nonequilibrium Criticality

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Heyl,  Markus
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Zunkovic, B., Heyl, M., Knap, M., & Silva, A. (2018). Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging Different Concepts of Nonequilibrium Criticality. Physical Review Letters, 120(13): 130601. doi:10.1103/PhysRevLett.120.130601.


Cite as: https://hdl.handle.net/21.11116/0000-0001-481B-1
Abstract
We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent alpha, which can be experimentally realized in ion traps. We focus on two classes of emergent dynamical critical phenomena following a quantum quench from a ferromagnetic initial state: The first one manifests in the time-averaged order parameter, which vanishes at a critical transverse field. We argue that such a transition occurs only for long-range interactions alpha <= 2. The second class corresponds to the emergence of time-periodic singularities in the return probability to the ground-state manifold which is obtained for all values of alpha and agrees with the order parameter transition for alpha <= 2. We characterize how the two classes of nonequilibrium criticality correspond to each other and give a physical interpretation based on the symmetry of the time-evolved quantum states.