论文标题
Bloch电子在蜂窝状晶格和曲曲面的calabi-yau几何形状上
Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry
论文作者
论文摘要
我们在均匀磁场的二维蜂窝晶状体上发现Bloch电子的光谱问题与曲折calabi-yau三倍的量子几何形状之间找到了新的关系。我们表明，Bloch电子的差方程与Calabi-yau三倍的量子镜曲线相同。作为一种应用，我们表明，弱磁通磁通状态中电子光谱的带宽是由在nekrasov-shatashvili限制中的conifold单数点处的拓扑弦乐自由能系统计算的。
We find a new relation between the spectral problem for Bloch electrons on a two-dimensional honeycomb lattice in a uniform magnetic field and that for quantum geometry of a toric Calabi-Yau threefold. We show that a difference equation for the Bloch electron is identical to a quantum mirror curve of the Calabi-Yau threefold. As an application, we show that bandwidths of the electron spectra in the weak magnetic flux regime are systematically calculated by the topological string free energies at conifold singular points in the Nekrasov-Shatashvili limit.
