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Finite Speed of Quantum Information in Models of Interacting Bosons at Finite Density
Physical Review X ( IF 12.5 ) Pub Date : 2022-05-17 , DOI: 10.1103/physrevx.12.021039
Chao Yin, Andrew Lucas

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 the density matrix ρexp[μN] (with N the total boson number), ensemble-averaged correlators of the form [A0,Br(t)], along with out-of-time-ordered correlators, must vanish as the distance r between two local operators grows, unless tr/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 [A0,Br(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.

中文翻译:

有限密度相互作用玻色子模型中量子信息的有限速度

我们证明了量子信息在任何相互作用的玻色子模型中以有限的速度传播,其(可能是时间相关的)哈密顿量包含空间局部单玻色子跳跃项以及任意局部密度相关的相互作用。更准确地说,使用密度矩阵ρ经验[-μñ](和ñ总玻色子数),整体平均相关器的形式[一种0,r()], 连同时间不齐的相关器, 必须随着距离消失r两个本地运营商之间的增长,除非r/v对于一些有限的速度v. 在一维模型中,我们对该结果进行了有用的扩展,证明了换向器的所有矩阵元素的小[一种0,r()]如果在有限密度状态之间/r足够小。我们的界限与实验实现的相互作用玻色子模型中的物理现实初始条件相关。特别是,我们证明v在 Bose-Hubbard 模型中,数字密度的缩放速度不会快于线性:这种缩放与之前在高密度限制中的结果相匹配。我们证明背后的量子行走形式主义提供了一种在具有无界算子和无限维希尔伯特空间的模型中限制量子动力学的替代方法,其中李布-罗宾逊界一直难以证明。
更新日期:2022-05-18
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