Hierarchy of Linear Light Cones with Long-Range Interactions

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a ma...

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Autores principales:	Minh C. Tran, Chi-Fang Chen, Adam Ehrenberg, Andrew Y. Guo, Abhinav Deshpande, Yifan Hong, Zhe-Xuan Gong, Alexey V. Gorshkov, Andrew Lucas
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/5a6be182fb564d49a2d8df81385553ca
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spelling	oai:doaj.org-article:5a6be182fb564d49a2d8df81385553ca2021-12-02T11:11:32ZHierarchy of Linear Light Cones with Long-Range Interactions10.1103/PhysRevX.10.0310092160-3308https://doaj.org/article/5a6be182fb564d49a2d8df81385553ca2020-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.031009http://doi.org/10.1103/PhysRevX.10.031009https://doaj.org/toc/2160-3308In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state \|ψ⟩, O_{x}(t)O_{y}\|ψ⟩≈O_{y}O_{x}(t)\|ψ⟩ with arbitrarily small errors—so long as \|x-y\|≳vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/r^{α}. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same α, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state \|ψ⟩ when α>3 (Lieb-Robinson light cone); for a typical state \|ψ⟩ chosen uniformly at random from the Hilbert space when α>5/2 (Frobenius light cone); and for every state of a noninteracting system when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.Minh C. TranChi-Fang ChenAdam EhrenbergAndrew Y. GuoAbhinav DeshpandeYifan HongZhe-Xuan GongAlexey V. GorshkovAndrew LucasAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 3, p 031009 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Minh C. Tran Chi-Fang Chen Adam Ehrenberg Andrew Y. Guo Abhinav Deshpande Yifan Hong Zhe-Xuan Gong Alexey V. Gorshkov Andrew Lucas Hierarchy of Linear Light Cones with Long-Range Interactions
description	In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state \|ψ⟩, O_{x}(t)O_{y}\|ψ⟩≈O_{y}O_{x}(t)\|ψ⟩ with arbitrarily small errors—so long as \|x-y\|≳vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/r^{α}. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same α, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state \|ψ⟩ when α>3 (Lieb-Robinson light cone); for a typical state \|ψ⟩ chosen uniformly at random from the Hilbert space when α>5/2 (Frobenius light cone); and for every state of a noninteracting system when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.
format	article
author	Minh C. Tran Chi-Fang Chen Adam Ehrenberg Andrew Y. Guo Abhinav Deshpande Yifan Hong Zhe-Xuan Gong Alexey V. Gorshkov Andrew Lucas
author_facet	Minh C. Tran Chi-Fang Chen Adam Ehrenberg Andrew Y. Guo Abhinav Deshpande Yifan Hong Zhe-Xuan Gong Alexey V. Gorshkov Andrew Lucas
author_sort	Minh C. Tran
title	Hierarchy of Linear Light Cones with Long-Range Interactions
title_short	Hierarchy of Linear Light Cones with Long-Range Interactions
title_full	Hierarchy of Linear Light Cones with Long-Range Interactions
title_fullStr	Hierarchy of Linear Light Cones with Long-Range Interactions
title_full_unstemmed	Hierarchy of Linear Light Cones with Long-Range Interactions
title_sort	hierarchy of linear light cones with long-range interactions
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/5a6be182fb564d49a2d8df81385553ca
work_keys_str_mv	AT minhctran hierarchyoflinearlightconeswithlongrangeinteractions AT chifangchen hierarchyoflinearlightconeswithlongrangeinteractions AT adamehrenberg hierarchyoflinearlightconeswithlongrangeinteractions AT andrewyguo hierarchyoflinearlightconeswithlongrangeinteractions AT abhinavdeshpande hierarchyoflinearlightconeswithlongrangeinteractions AT yifanhong hierarchyoflinearlightconeswithlongrangeinteractions AT zhexuangong hierarchyoflinearlightconeswithlongrangeinteractions AT alexeyvgorshkov hierarchyoflinearlightconeswithlongrangeinteractions AT andrewlucas hierarchyoflinearlightconeswithlongrangeinteractions
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Hierarchy of Linear Light Cones with Long-Range Interactions

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