Computation of ESR spectra from the time evolution of the magnetization: Comparison of autocorrelation and Wiener-Khinchin-relation-based methods
Computation of ESR spectra from the time evolution of the magnetization: Comparison of autocorrelation and Wiener-Khinchin-relation-based methods
复制标题
根据磁化强度随时间的演化计算 ESR 谱：自相关法和基于 Wiener-Khinchin 关系的方法的比较
DOI：
10.1103/physrevb.92.214431
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
S. Miyashita
中科院分区：
文献类型：
--
作者：
H. Ikeuchi;H. De Raedt;S. Bertaina;S. Miyashita
具体晶体构型的有限温度电子自旋共振（ESR）谱的计算是量子自旋系统研究中的一个非常重要的问题。虽然直接评估的Kubo公式的数值对角化的手段产生精确的结果，内存和CPU时间的限制，这种方法的适用性小系统的大小。基于单个纯量子态的时间演化的方法可以用于研究更大的系统。一种这样的方法利用了这样的性质，即对于所谓的热典型状态的几个样本获得的自相关函数的期望值产生热平衡值的良好估计。本文提出了一种基于类Wiener-Khinchin定理的量子系统的新方法。通过与精确对角化结果的比较，表明这两种方法都能得到正确的结果。由于基于Wiener-Khinchin的方法涉及对热典型状态的采样，因此我们研究了采样分布的统计特性。由于有限的观测时间的影响进行了研究，发现这两种方法不同，但它也被发现，对于这两种方法，随着系统尺寸的增加，效果消失。本文给出了一维XXZ海森堡链的ESR谱，并讨论了双峰间距与链长的关系。
The calculation of finite temperature electron spin resonance (ESR) spectra for concrete specified crystal configurations is a very important issue in the study of quantum spin systems. Although direct evaluation of the Kubo formula by means of numerical diagonalization yields exact results, memory and CPU time restrictions limit the applicability of this approach to small system sizes. Methods based on the time evolution of a single pure quantum state can be used to study larger systems. One such method exploits the property that the expectation value of the autocorrelation function obtained for a few samples of so-called thermal typical states yields a good estimate of the thermal equilibrium value. In this paper, we propose a new method based on a Wiener-Khinchin-like theorem for quantum system. By comparison with exact diagonalization results, it is shown that both methods yield correct results. As the Wiener-Khinchin-based method involves sampling over thermal typical states, we study the statistical properties of the sampling distribution. Effects due to finite observation time are investigated and found to differ for the two methods but it is also found that, for both methods, the effects vanish as the system size increases. We present ESR spectra of the one-dimensional XXZ Heisenberg chain of up to 28 spins and discuss the dependence of separation of double peaks on the chain length.