论文标题
具有远距离相互作用的量子旋转系统的离散截短的Wigner近似的性能评估
Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions
论文作者
论文摘要
离散的截短Wigner近似（DTWA）是分析量子自旋系统动力学的强大工具。由于DTWA包括对平均场近似的前阶量子校正，因此自然可以预期，当系统的相互作用范围增加时，DTWA会变得更加准确。但是，仍然缺乏对这种期望的定量佐证，主要是因为在大型系统中通常很难评估DTWA定量有效的时间表。为了研究有效性时间尺度如何取决于相互作用范围，我们通过DTWA及其扩展（包括二阶校正）分析了量子旋转模型的量子自旋模型的动力学，该动力学通过磁场突然淬火，该动力学从Bogoliubov-born-born-Born-born-born-born-green-kirkwood-kirkwood-kirkwood-kirkwood-kirkwood-kirkwood-kirkwood-yvon-yvon-yvon均等。我们还开发了一种用于计算DTWA框架内的二阶Rényi熵的公式。通过比较DTWA计算出的Rényi熵的时间演变与通过扩展（包括校正）的时间演化，我们发现在一维系统和二维系统中，有效性时间尺度随着步骤函数类型相互作用的范围而言，有效性时间表都会增加代数。
The discrete truncated Wigner approximation (DTWA) is a powerful tool for analyzing dynamics of quantum spin systems. Since the DTWA includes the leading-order quantum corrections to a mean-field approximation, it is naturally expected that the DTWA becomes more accurate when the range of interactions of the system increases. However, quantitative corroboration of this expectation is still lacking mainly because it is generally difficult in a large system to evaluate a timescale on which the DTWA is quantitatively valid. In order to investigate how the validity timescale depends on the interaction range, we analyze dynamics of quantum spin models with a step function type interaction subjected to a sudden quench of a magnetic field by means of both DTWA and its extension including the second-order correction, which is derived from the Bogoliubov-Born-Green-Kirkwood-Yvon equation. We also develop a formulation for calculating the second-order Rényi entropy within the framework of the DTWA. By comparing the time evolution of the Rényi entropy computed by the DTWA with that by the extension including the correction, we find that both in the one- and two-dimensional systems the validity timescale increases algebraically with the range of the step function type interaction.
