Hierarchy of Linear Light Cones with Long-Range Interactions
Hierarchy of Linear Light Cones with Long-Range Interactions
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DOI：
10.1103/physrevx.10.031009
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发表时间：
2020-01
影响因子：
12.5
通讯作者：
Minh C. Tran;Chi-Fang Chen;Adam Ehrenberg;Andrew Y. Guo;A. Deshpande;Yifan Hong;Zhexuan Gong;A. Gorshkov;A. Lucas
中科院分区：
文献类型：
--
作者：
Minh C. Tran;Chi-Fang Chen;Adam Ehrenberg;Andrew Y. Guo;A. Deshpande;Yifan Hong;Zhexuan Gong;A. Gorshkov;A. Lucas
在具有局域相互作用的量子多体系统中，量子信息和纠缠不能扩散到线性光锥之外，线性光锥以类似于光速的紧急速度膨胀。在充分分开的时空点处的局部运算近似可交换--给定一个多体状态，$\mathcal{O}_x(T)\mathcal{O}_y|\psi\Range\Approx\mathcal{O}_y\mathcal{O}_x(T)|\psi\Rangel$--只要$|x-y|\gtrsim Vt$，其中$v$是有限的。然而，自然界中实现的大多数非相对论物理系统都有长程相互作用：相隔一段距离的两个自由度与势能$V(R)\proto 1/r^{\α}$相互作用。在具有长程相互作用的系统中，我们严格地建立了线性光锥的层次结构：在相同的值下，一些量子信息处理任务受线性光锥的约束，而另一些则不受约束。在一个空间维度中，当$\α&>3$(Lieb-Robinson光锥)；时，对于从希尔伯特空间中均匀随机选择的典型态，当$\α&>3$(Lieb-Robinson光锥)；时，对于非相互作用系统的每个状态，当$\α&>2$(自由光锥)时，对于非相互作用系统的每一种状态，这个线性光锥都存在。这些界适用于依赖时间的系统，并且在子代数改进之前是最优的。我们关于Lieb-Robinson和自由光锥的定理--以及它们的紧密性--也可以推广到任意维度。我们讨论了我们的界限对连通相关器的增长和拓扑序的增长、有隙系统中关联的聚集以及具有远程相互作用的系统的数字模拟的影响。此外，我们还证明了普适量子态转移和多体量子混沌都受Frobenius光锥的约束，因此不受所有Lieb-Robinson界的约束。
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, $\mathcal{O}_x(t) \mathcal{O}_y |\psi\rangle \approx \mathcal{O}_y\mathcal{O}_x(t) |\psi\rangle$ with arbitrarily small errors -- so long as $|x-y|\gtrsim vt$, where $v$ is finite. 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 $V(r) \propto 1/r^{\alpha}$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same $\alpha$, 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 when $\alpha>3$ (Lieb-Robinson light cone); for a typical state chosen uniformly at random from the Hilbert space when $\alpha>\frac{5}{2}$ (Frobenius light cone); for every state of a non-interacting system when $\alpha>2$ (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, are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.