Finite Speed of Quantum Information in Models of Interacting Bosons at Finite Density
Finite Speed of Quantum Information in Models of Interacting Bosons at Finite Density
复制标题
有限密度相互作用玻色子模型中量子信息的有限速度
DOI：
10.1103/physrevx.12.021039
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发表时间：
2021
影响因子：
12.5
通讯作者：
A. Lucas
中科院分区：
文献类型：
--
作者：
Chao Yin;A. Lucas
我们证明了在任何相互作用玻色子模型中，量子信息以finite速度传播，该相互作用玻色子模型的哈密顿量(可能依赖于时间)包含空间局域单玻色子跳跃项和任意局域密度相关相互作用。更准确地说，对于密度矩阵ρ∝exp[−µN](其中N是总玻色子数)，形式为(Cid：104)[A0，Brr(T)](Cid：105)的系综平均相关器以及无序相关器必须随着两个局部算符之间的距离r的增长而消失，除非t≥r/v为某个finite速度v。在一维模型中，我们给出了这一结果的一个有用的推广，证明了当t/r确实很小时，在finite密度态之间的交换子[A0，Brr(T)]的所有矩阵元是小的。我们的界限与实验实现的相互作用玻色子模型中物理上真实的初始条件有关。特别地，我们证明了在Bose-Hubbard模型中，v的标度不会比数密度的线性标度快：这个标度与以前在高密度极限下的结果相吻合。我们证明背后的量子漫步形式为在具有无界算子的模型和finite维希尔伯特空间中约束量子动力学提供了另一种方法，在这些空间中，lib-Robinson界的证明一直是出了名的具有挑战性。
We prove that quantum information propagates with a finite velocity in any model of interacting bosons whose (possibly time-dependent) Hamiltonian contains spatially local single-boson hopping terms along with arbitrary local density-dependent interactions. More precisely, with density matrix ρ ∝ exp[ − µN ] (with N the total boson number), ensemble averaged correlators of the form (cid:104) [ A 0 , B r ( t )] (cid:105) , along with out-of-time-ordered correlators, must vanish as the distance r between two local operators grows, unless t ≥ r/v for some finite speed v . In one dimensional models, we give a useful extension of this result that demonstrates the smallness of all matrix elements of the commutator [ A 0 , B r ( t )] between finite density states if t/r is sufficiently small. Our bounds are relevant for physically realistic initial conditions in experimentally realized models of interacting bosons. In particular, we prove that v can scale no faster than linear in number density in the Bose-Hubbard model: this scaling matches previous results in the high density limit. The quantum walk formalism underlying our proof provides an alternative method for bounding quantum dynamics in models with unbounded operators and infinite-dimensional Hilbert spaces, where Lieb-Robinson bounds have been notoriously challenging to prove.
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影响因子：
12.5
作者：
Minh C. Tran;Chi-Fang Chen;Adam Ehrenberg;Andrew Y. Guo;A. Deshpande;Yifan Hong;Zhexuan Gong;A. Gorshkov;A. Lucas
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
收紧局部交互系统中的利布-罗宾逊约束
影响因子：
9.7
作者：
Wang, Zhiyuan;Hazzard, Kaden R.A.
通讯作者：
Hazzard, Kaden R.A.
影响因子：
19.6
作者：
Brandão F
通讯作者：
Brandão F
影响因子：
2.9
作者：
Else, Dominic, V;Machado, Francisco;Yao, Norman Y.
通讯作者：
Yao, Norman Y.