摘要翻译:
我们解析地得到了自旋1/2Heisenberg XXZ链在$\delta=1/2$处直到六个晶格位的所有密度矩阵元。我们使用Jimbo和Miwa导出的无质量XXZ链相关函数的多重积分公式。对于自旋-自旋关联函数,我们新得到了四邻和五邻横向关联函数。我们计算了密度矩阵的所有特征值,并分析了特征值分布。利用这些结果,得到了六个晶格位上约化密度矩阵的纠缠熵的精确值。我们观察到,我们的精确结果与共形场论所预言的渐近公式相当吻合。
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英文标题:
《Density matrix elements and entanglement entropy for the spin-1/2 XXZ
chain at $\Delta$=1/2》
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作者:
Jun Sato, Masahiro Shiroishi
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最新提交年份:
2007
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分类信息:
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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英文摘要:
We have analytically obtained all the density matrix elements up to six lattice sites for the spin-1/2 Heisenberg XXZ chain at $\Delta=1/2$. We use the multiple integral formula of the correlation function for the massless XXZ chain derived by Jimbo and Miwa. As for the spin-spin correlation functions, we have newly obtained the fourth- and fifth-neighbour transverse correlation functions. We have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. Using these results the exact values of the entanglement entropy for the reduced density matrix up six lattice sites have been obtained. We observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory.
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PDF链接:
https://arxiv.org/pdf/704.085