Calabi-Yau geometry and electrons on 2d lattices

@article{Hatsuda2017CalabiYauGA,
  title={Calabi-Yau geometry and electrons on 2d lattices},
  author={Yasuyuki Hatsuda and Yuji Sugimoto and Zhaojie Xu},
  journal={Physical Review D},
  year={2017},
  volume={95}
}
The B-model approach of topological string theory leads to difference equations by quantizing algebraic mirror curves. It is known that these quantum mechanical systems are solved by the refined topological strings. Recently, it was pointed out that the quantum eigenvalue problem for a particular Calabi--Yau manifold, known as local $\mathbb{F}_0$, is closely related to the Hofstadter problem for electrons on a two-dimensional square lattice. In this paper, we generalize this idea to a more… 

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