Title: Constructing optimal Wannier functions via potential theory: isolated single band for matrix models Show Chinese title

Title: 通过势论构造最优Wannier函数：矩阵模型的孤立单带

Abstract: We present a rapidly convergent scheme for computing globally optimal Wannier functions of isolated single bands for matrix models in two dimensions. The scheme proceeds first by constructing provably exponentially localized Wannier functions directly from parallel transport (with simple analytically computable corrections) when topological obstructions are absent. We prove that the corresponding Wannier functions are real when the matrix model possesses time-reversal symmetry. When a band has a nonzero Berry curvature, the resulting Wannier function is not optimal, but it is transformed into the global optimum by a single gauge transformation that eliminates the divergence of the Berry connection. Complete analysis of the construction is presented, paving the way for further improvements and generalizations. The performance of the scheme is illustrated with several numerical examples. Show Chinese abstract

Abstract: 我们提出了一种快速收敛的方案，用于计算二维矩阵模型中孤立单带的全局最优Wannier函数。 该方案首先通过构建明确指数局部化的Wannier函数开始（用简单的解析可计算校正），当不存在拓扑障碍时，这些函数可以直接从平行传输获得。 我们证明，当矩阵模型具有时间反演对称性时，相应的Wannier函数是实值的。 当一个能带具有非零Berry曲率时，所得到的Wannier函数不是最优的，但可以通过单一规范变换将其转换为全局最优，该变换消除了Berry联络的发散。 完整的构造分析被呈现出来，为进一步改进和推广铺平了道路。 该方案的性能通过多个数值例子进行了说明。