Time-polynomial Lieb-Robinson bounds for finite-range spin-network models
Time-polynomial Lieb-Robinson bounds for finite-range spin-network models
复制标题
有限范围自旋网络模型的时间多项式 Lieb-Robinson 界限
DOI：
10.1103/physreva.100.052309
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发表时间：
2019
影响因子：
2.9
通讯作者：
V. Giovannetti
中科院分区：
文献类型：
--
作者：
S. Chessa;V. Giovannetti
Lieb-Robinson束缚为信息在非相对论量子自旋网络中的传播速度设定了一个理论上限。在其原始版本中，它导致演化时间的指数爆炸函数，这部分地通过指数递减项来缓解，该指数递减项取决于信号覆盖的距离（两个指数之间的比率有效地定义了传播速度的上限）。在本文中，通过适当地考虑模型的自由参数，我们展示了如何将这种结构转化为一个更强的不等式，其中上限只与演化时间成多项式关系。我们的分析适用于网络的任何选择的拓扑结构，只要相关的相互作用的范围是显式有限的。对于特殊情况下的线性自旋网络，我们也提出了一个替代推导的基础上微扰展开的方法，改善了以前的不等式。在同一背景下，我们还建立了一个下界的信息传播的速度，至少在小的传播时间的限制，产生一个非平凡的结果。
The Lieb-Robinson bound sets a theoretical upper limit on the speed at which information can propagate in nonrelativistic quantum spin networks. In its original version, it results in an exponentially exploding function of the evolution time, which is partially mitigated by an exponentially decreasing term that instead depends upon the distance covered by the signal (the ratio between the two exponents effectively defining an upper bound on the propagation speed). In the present paper, by properly accounting for the free parameters of the model, we show how to turn this construction into a stronger inequality where the upper limit only scales polynomially with respect to the evolution time. Our analysis applies to any chosen topology of the network, as long as the range of the associated interaction is explicitly finite. For the special case of linear spin networks we present also an alternative derivation based on a perturbative expansion approach which improves the previous inequality. In the same context we also establish a lower bound to the speed of the information spread which yields a nontrivial result at least in the limit of small propagation times.
影响因子：
2.9
作者：
Burrell C
通讯作者：
Burrell C