Efficient computation of lattice Green's functions for models with nearest-neighbour hopping
Efficient computation of lattice Green's functions for models with nearest-neighbour hopping
复制标题
具有最近邻跳跃模型的格子格林函数的高效计算
DOI：
10.1209/0295-5075/92/40003
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
A. Cook
中科院分区：
文献类型：
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作者：
M. Berciu;A. Cook
我们表明，最近邻（nn）跳跃模型，晶格绿色的功能，可以计算，而不需要进行积分。我们的方法适用于矩形，三角形和蜂窝格子在二维，并在三维简单，面心和体心格子。外部磁场可以简单地处理。作为一个例子，我们表明，我们的方法适用于任何比例的磁通量通过的单位单元，即，无论在磁性单位单元的大小的变化。其他简单的概括是每个位点具有多个轨道的模型，具有任何自旋-轨道耦合，原位无序及其任何组合。该方法同样适用于存在曲面的情况。在所有情况下，可以非常有效地获得大距离的精确值，并且没有有限尺寸效应。并分析了它与其它计算方法的关系。
We show that for models with nearest-neighbour (nn) hopping, the lattice Green's functions can be calculated without the need to perform integrals. Our method applies to rectangular, triangular and honeycomb lattices in two dimensions, and to simple, face-centered and body-centered lattices in three dimensions. External magnetic fields can be dealt with trivially. As an example, we show that our method works for any ratio ϕ/ϕ0 of the magnetic flux through the unit cell, i.e. irrespective of the change in the size of the magnetic unit cell. Other straightforward generalizations are to models with multiple orbitals per site, with any spin-orbit coupling, on-site disorder, and any combinations thereof. The method works equally well in the presence of surfaces. In all cases, accurate values for large distances can be obtained very efficiently and without finite-size effects. The relationship to other computational methods is also analyzed.