Cluster Transfer Matrix Method and Quantum Statistical Mechanics of Spin Systems

自旋系统的簇传递矩阵方法与量子统计力学

• 批准号: 61540253
• 负责人: TSUZUKI Toshio
• 金额: $ 1.02万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1987
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540253/
• 关键词: Cluster transfer matrix method; quantum effect; Trotter formula; Heisenberg spin chain; specific heat and susceptibility; magnetic field effect; magnon; spin coherent state; tunneling splitting and quantum coherence; ソリトン系の統計力学; 磁場下一次元ハイゼンベルグ系 /

1. The main part of this project is to develope a method on the basis of the Suzuki-Trotter formula, by which we can compute the quantum effect on thermodynamics of one-dimensional spin systems down to very low temperature t K_BT/2JS^2-0.1. We have observed that the correlation among spins, which is produced by the nearest neighbour exchange coupling -2J in the present case, grows up long distance with decreasing t, so that the size of decomposition for applying the Suzuki-Trotter formula should be set to be as large as the correlation length at temperature down to which one want to compute the thermodynamics. This idea has lead us the cluster transfer matrix method. An analytical application to S = 1/2 XY model has shown a good improvement of numerical computation even in the case of 3 spin cluster plus Trotter number M = 6, on comparing the results with exact ones. For S = 1/2 Heisenberg model we have obtained satisfactory results of susceptibility and specific heat down to t - 0.1 in the ferromagnetic case by taking 4 spin cluster plus M = 6, but not so satisfactory results in teh antiferromagnetic case. We have to enlarge both the size of cluster and M in the latter case.2. We have presented an analytic formula of computing the tunnelling splitting in some kinds of quantum spin system without going to the semiclassical limit. The splitting of energy levels is the characteristic frequency of quantum coherence to be seen in spin systems under consideration.3. An extensive review of statistical mechanics of soliton bearing systems has been presented. This review has been intended to be available as an introductory course to the present field of physics.

1.本项目的主要内容是在铃木-特罗特公式的基础上发展一种方法，通过该方法我们可以计算一维自旋系统的量子热力学效应，直到非常低的温度t K_BT/2 JS ^[2 -0.1]。我们已经观察到，自旋之间的相关性，这是由最近邻交换耦合-2J在目前的情况下，随着t的减小，增长了很长的距离，因此，应用铃木-特罗特公式的分解的大小应该设置为与相关长度一样大的温度下，人们想要计算热力学。这一思想导致了我们的集群转移矩阵法。对S = 1/2XY模型的分析表明，即使在3自旋集团加Trotter数M = 6的情况下，数值计算结果与精确计算结果相比也有很大的改进。对于S = 1/2的海森堡模型，取4自旋团簇加M = 6，在铁磁情况下得到了磁化率和比热的满意结果，直到t - 0.1，而在反铁磁情况下则不太满意.在后一种情况下，我们必须同时增大簇的大小和M.本文给出了计算几类量子自旋系统的隧穿劈裂的解析公式，而不必进入半经典极限。能级的分裂是自旋系统在双光子作用下量子相干的特征频率.本文对孤立子轴承系统的统计力学作了广泛的评述。这篇评论旨在作为目前物理学领域的入门课程。

项目成果

T.Tszuuki: Progress of Theoretical Physics. 75. 225-242 (1986)

T.Tszuuki：理论物理学的进展。

Toshio,TSUZUKI: Progress of Theoretical Physics. 76. 52-66 (1986)

都筑敏夫：理论物理学进展。

T.Tsuzuki: Proceeding of the Workshop on Magnetic Excitations and Fluctuations【II】. (1987)

T.Tsuzuki：磁激励和涨落研讨会论文集【II】（1987）。

Toshio TSUZUKI: "An Improved Transfer Matrix Method for Quantum Spin Systems" Progress of Theoretical Physics. 73. 1352-1368 (1985)

Toshio TSUZUKI：“量子自旋系统的改进传递矩阵方法”理论物理进展。

Toshio TSUZUKI: "On a Symmetric (2S+1)-State System Coupled to Its Environment: Tunniling Splitting and Quantum Coherence" Proceeding of the Workshop on Magnetic Excitations and Fluctuations II (Torino, Italy, 1987). 65-69 (1987)

Toshio TSUZUKI：“论与其环境耦合的对称 (2S 1) 态系统：隧道分裂和量子相干性”磁激发和涨落 II 研讨会论文集（意大利都灵，1987 年）。