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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American Physical Society
2020
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oai:doaj.org-article:7654f5d784f44cf2b8ab1f277607fd2c2021-12-02T11:11:32ZStrictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions10.1103/PhysRevX.10.0310102160-3308https://doaj.org/article/7654f5d784f44cf2b8ab1f277607fd2c2020-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.031010http://doi.org/10.1103/PhysRevX.10.031010https://doaj.org/toc/2160-3308In 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.Tomotaka KuwaharaKeiji SaitoAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 3, p 031010 (2020) |
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DOAJ |
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DOAJ |
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EN |
| topic |
Physics QC1-999 |
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Physics QC1-999 Tomotaka Kuwahara Keiji Saito Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions |
| description |
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. |
| format |
article |
| author |
Tomotaka Kuwahara Keiji Saito |
| author_facet |
Tomotaka Kuwahara Keiji Saito |
| author_sort |
Tomotaka Kuwahara |
| title |
Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions |
| title_short |
Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions |
| title_full |
Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions |
| title_fullStr |
Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions |
| title_full_unstemmed |
Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions |
| title_sort |
strictly linear light cones in long-range interacting systems of arbitrary dimensions |
| publisher |
American Physical Society |
| publishDate |
2020 |
| url |
https://doaj.org/article/7654f5d784f44cf2b8ab1f277607fd2c |
| work_keys_str_mv |
AT tomotakakuwahara strictlylinearlightconesinlongrangeinteractingsystemsofarbitrarydimensions AT keijisaito strictlylinearlightconesinlongrangeinteractingsystemsofarbitrarydimensions |
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1718396168273133568 |