02312nas a2200217 4500008004100000245006500041210006400106260001400170490000700184520168700191100001901878700001901897700002001916700002001936700002301956700001601979700001901995700002502014700001802039856003702057 2020 eng d00aHierarchy of linear light cones with long-range interactions0 aHierarchy of linear light cones with longrange interactions c5/29/20200 v103 a
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. Yet most non-relativistic 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/rα. 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, commutators of local operators 〈ψ|[Ox(t),Oy]|ψ〉 are negligible in every state |ψ〉 when |x−y|≳vt, where v is finite when α>3 (Lieb-Robinson light cone); in a typical state |ψ〉 drawn from the infinite temperature ensemble, v is finite when α>52 (Frobenius light cone); in non-interacting systems, v is finite in every state 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 quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.
1 aTran, Minh, C.1 aChen, Chi-Fang1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aDeshpande, Abhinav1 aHong, Yifan1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V.1 aLucas, Andrew uhttps://arxiv.org/abs/2001.11509