# 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…

## 27 Citations

### Quantum curves and q-deformed Painlevé equations

- MathematicsLetters in Mathematical Physics
- 2019

We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve, these are…

### Quantum mirror curve of periodic chain geometry

- MathematicsJournal of High Energy Physics
- 2019

A bstractThe mirror curves enable us to study B-model topological strings on noncompact toric Calabi-Yau threefolds. One of the method to obtain the mirror curves is to calculate the partition…

### Quantum periods and spectra in dimer models and Calabi-Yau geometries

- Mathematics, PhysicsJournal of High Energy Physics
- 2020

We study a class of quantum integrable systems derived from dimer graphs and also described by local toric Calabi-Yau geometries with higher genus mirror curves, generalizing some previous works on…

### Topological string theory and applications

- Mathematics
- 2019

This thesis focuses on various applications of topological string theory based on different types of Calabi-Yau (CY) manifolds. The first type considered is the toric CY manifold, which is intimately…

### Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry

- Physics, Mathematics
- 2020

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…

### Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry

- Physics, MathematicsJournal of High Energy Physics
- 2020

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…

### Non-perturbative Quantum Mechanics from Non-perturbative Strings

- PhysicsAnnales Henri Poincaré
- 2018

This work develops a new method to calculate non-perturbative corrections in one-dimensional Quantum Mechanics, based on trans-series solutions to the refined holomorphic anomaly equations of…

### Quantum geometry of resurgent perturbative/nonperturbative relations

- Physics
- 2017

A bstractFor a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from…

### Quantized mirror curves and resummed WKB

- MathematicsJournal of High Energy Physics
- 2019

Based on previous insights, we present an ansatz to obtain quantization conditions and eigenfunctions for a family of difference equations which arise from quantized mirror curves in the context of…

### Quantized mirror curves and resummed WKB

- MathematicsJournal of High Energy Physics
- 2019

A bstractBased on previous insights, we present an ansatz to obtain quantization conditions and eigenfunctions for a family of difference equations which arise from quantized mirror curves in the…

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