Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions
In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded, and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial wh...
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| Auteurs principaux: | , |
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| Format: | article |
| Langue: | EN |
| Publié: |
American Physical Society
2020
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| Accès en ligne: | https://doaj.org/article/7654f5d784f44cf2b8ab1f277607fd2c |
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| Résumé: | In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded, and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial whether such a linear light cone exists. Herein, we consider generic long-range interacting systems with decaying interactions, such as R^{-α} with distance R. We prove the existence of the linear light cone for α>2D+1 (D, the spatial dimension), where we obtain the Lieb-Robinson bound as ∥[O_{i}(t),O_{j}]∥≲t^{2D+1}(R-v[over ¯]t)^{-α} with v[over ¯]=O(1) for two arbitrary operators O_{i} and O_{j} separated by a distance R. Moreover, we provide an explicit quantum-state transfer protocol that achieves the above bound up to a constant coefficient and violates the linear light cone for α<2D+1. In the regime of α>2D+1, our result characterizes the best general constraints on the information spreading. |
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