Dynamical simulation of integrable and nonintegrable models in the Heisenberg picture.
Dynamical simulation of integrable and nonintegrable models in the Heisenberg picture.
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DOI：
10.1103/physrevlett.106.077202
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发表时间：
2010-09
影响因子：
8.6
通讯作者：
D. Muth;R. Unanyan;M. Fleischhauer
中科院分区：
文献类型：
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作者：
D. Muth;R. Unanyan;M. Fleischhauer
量子多体动力学的数值模拟通常受到纠缠随时间线性增长的限制。最近的数值研究表明，对于一维贝特可积模型，海森堡图像中的局部算子的模拟是有效的。使用自旋1/2 XX链作为可映射到自由费米子的可积模型的一般例子，我们对此提供了一个简单的解释。我们还表明，同样的复杂性降低适用于具有高温自相关函数的算子，该自相关函数的衰减速度比指数慢，即，一个幂律。因此，单个守恒定律可能已经暗示了有效的可模拟性，正如我们将用数值方法说明自旋为1的XXZ模型一样。
The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown that for 1D Bethe-integrable models the simulation of local operators in the Heisenberg picture can be efficient. Using the spin-1/2 XX chain as generic example of an integrable model that can be mapped to free fermions, we provide a simple explanation for this. We show furthermore that the same reduction of complexity applies to operators that have a high-temperature autocorrelation function which decays slower than exponential, i.e., with a power law. Thus efficient simulability may already be implied by a single conservation law as we will illustrate numerically for the spin-1 XXZ model.