Simulating typical entanglement with many-body Hamiltonian dynamics
Simulating typical entanglement with many-body Hamiltonian dynamics
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模拟多体哈密顿动力学的典型纠缠
DOI：
10.1103/physreva.84.052321
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发表时间：
2011
影响因子：
2.9
通讯作者：
M.Murao
中科院分区：
文献类型：
--
作者：
Y.Nakata;M.Murao
研究了由多体相互作用构成的一维自旋1/2伊辛型哈密顿量所产生的纠缠量的时间演化。我们通过分析几种类型的与时间无关的哈密顿量产生的纠缠量的分布来研究在时间演化过程中随机选择的态集合。我们将这种纠缠分布与典型的纠缠分布进行了比较，纠缠是从Hilbert空间中随机选择的一组态相对于酉不变性度量的纠缠。我们证明，如果哈密顿量包含适当的多体相互作用，则由与时间无关的哈密顿量得到的纠缠分布可以模拟典型纠缠的平均和标准差。我们还证明了对于某些类型的哈密顿量，达到这样的分布所需的时间是系统大小的多项式。
We study the time evolution of the amount of entanglement generated by one-dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.