Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions

Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions
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DOI：
10.1103/physrevresearch.3.013060
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发表时间：
2020-08
期刊：
arXiv: Quantum Gases
影响因子：
--
通讯作者：
M. Kunimi;Kazuma Nagao;S. Goto;I. Danshita
M. Kunimi;Kazuma Nagao;S. Goto;I. Danshita
中科院分区：
其他
文献类型：
--
作者：
M. Kunimi;Kazuma Nagao;S. Goto;I. Danshita

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离散截断维格纳近似（DTWA）是分析量子自旋系统动力学的有力工具。由于DTWA包含了平均场近似的阶量子修正，所以当系统的相互作用范围增加时，DTWA自然会变得更加精确。然而，对这一期望的定量证实仍然缺乏，主要原因是在一个大系统中，通常很难评价DTWA在数量上有效的时间尺度。为了研究有效时间尺度如何依赖于相互作用范围，我们利用DTWA及其包含二阶修正的扩展（由Bogoliubov-Born-Green-Kirkwood-Yvon方程导出）来分析磁场突然猝灭作用下量子自旋模型的动力学。我们还开发了一个新的公式来计算二阶Renyi熵的框架内的DTWA。通过比较DTWA计算的Renyi熵与包含校正的扩展计算的Renyi熵的时间演化，我们发现在一维和二维系统中，有效时间尺度随着相互作用范围的增加而代数增加。
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 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 new formulation for calculating the second-order Renyi entropy within the framework of the DTWA. By comparing the time evolution of the Renyi 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 interaction range.