通常我们使用一阶Wilson loop的方法来计算 Wannier band,用于判别拓扑绝缘体(TIs)的拓扑性质, Z2 为0或者1,是否出现边缘态,trivial or non-trivial。Wilson loop方法可见之前的文章:zhuanlan.zhihu.com/p/69 高阶拓扑绝缘体(HOTIs)表现出不凡的拓扑性质:d维的拓扑绝缘体,其(d-1)维的局域态
我们计算(wannier)带极化数所用到的nested wilson loop取自Benalcazar的文章,首先我们定义沿x方向上的wilson线: 其中|μk> 是周期电场(TM模型下的Ez),满足 <μkm|ε|μkn>=δmn, 其中ε(x,y) 是介电常数, Δx=2πaNxX (设置a=1), Nx 是沿着x方向的单位原胞数量。 m,n∈1...Nocc 表示所需要的...
Wilson Bol + 5 for your first example, you can ignore the inner loop altogether as it does nothing { } - just pretend it isn't there - 'a' is incremented by the 'a++' and then output only within the main outer loop for each time it iterates (i.e. two times) ...
For the 3–loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3–loop anomalous dimensions.doi:10.1016/j.nuclphysbps.2008.09.109Johannes BlümleinElsevier B.V.Nuclear Physics BJ. Blu¨mlein, Nucl. Phys. Proc. Suppl. 183 (2008) 232 [arXiv:...
[15 Mar 2018 10:32] James Wilson We are running MySQL 5.7.21 on Ubuntu 16.04 with SugarCRM 7.9. Ok, this is a real problem for us. We host SugarCRM instances on our hosting platform. We are testing MySQL 5.7 with a few instances and would like to upgrade all. However, this bug is...
Wilson, A.T. Nasrabadi, S.O. Nielsen, Computing free energies using nested sampling-based approaches. Mol. Sim. 44, 1108 (2018) Google Scholar P.G. Bolhuis, G. Csányi, Nested transition path sampling. Phys. Rev. Lett. 120, 250601 (2018) ADS MathSciNet Google Scholar C. Dellago...
[44] with the finite part of the Wilson coefficient renormalization, we obtain for the Higgs finite remainders FLfiVn,gg(1, 2) |μ2=Q2 = αs 2π 5C A − 3CF FLM,gg(1, 2) + O( ), FLV 2,gg,fin(1, 2) |μ2=Q2 = αs 2π 2 β02π 2 + 5 2CA − 3 2CF 2 ×...
BBH模型和态密度分布参考这篇:BBH高阶拓扑绝缘体模型(附Python代码)。BBH模型和nested Wilson loop公式见参考文献[1-3]。本篇计算的nested Wilson loop仅仅是考虑能带非简并的情况。 一、能带 先画个能带。为了避免重复写代码,可以调用开源软件包Guan中的函数(https://py.guanjihuan.com)。
在极化的基础上，继续在另一个方向上做wilson loop，也就是嵌套（nested）wilson loop，得到的是电四极...
B.A. Wilson, L.D. Gelb, S.O. Nielsen, Nested sam- pling of isobaric phase space for the direct evaluation of the isothermal-isobaric partition function of atomic systems. J. Chem. Phys. 143, 154108 (2015) 83. A.D. Bruce, N.B. Wilding, Phys. Rev. Lett. 68, 193 (1992) 84. ...