Improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
Improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
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DOI：
10.1103/physreva.101.022333
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发表时间：
2020-02-26
影响因子：
2.9
通讯作者：
Yao, Norman Y.
中科院分区：
文献类型：
--
作者：
Else, Dominic, V;Machado, Francisco;Yao, Norman Y.
本文证明了具有长程相互作用的离散自旋系统的一族Lieb-Robinson界。我们的结果适用于任意的k体相互作用，只要它们衰减的幂律大于kd，其中d是系统的维数。更准确地说，我们要求作用在任何一个位置上的直径大于或等于R的项的范数之和按照幂律1/R-alpha衰减，其中alpha > d。这些界限使我们能够证明，在任何固定的时间，时间演化算子的空间衰减遵循任意接近1/r（alpha）。此外，我们引入了另一种光锥定义的幂律相互作用的量子系统，它捕获的区域的系统，改变哈密顿量可以影响本地运营商的演变。在短程相互作用系统中，这种光锥符合传统的定义。然而，在长程相互作用系统中，我们的定义产生了更严格的光锥，这在大多数物理环境中更相关。
In this paper, we prove a family of Lieb-Robinson bounds for discrete spin systems with long-range interactions. Our results apply for arbitrary k-body interactions, so long as they decay with a power law greater than kd, where d is the dimension of the system. More precisely, we require that the sum of the norm of terms with diameter greater than or equal to R, acting on any one site, decays as a power law 1/R-alpha, with alpha > d. These bounds allow us to prove that, at any fixed time, the spatial decay of a time evolved operator follows arbitrarily closely to 1/r(alpha). Moreover, we introduce an alternative light cone definition for power-law interacting quantum systems which captures the region of the system where changing the Hamiltonian can affect the evolution of a local operator. In short-range interacting systems, this light cone agrees with the conventional definition. However, in long-range interacting systems, our definition yields a stricter light cone, which is more relevant in most physical contexts.