Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry

Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry

Abstract 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 mirro...

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Main Authors: Yasuyuki Hatsuda, Yuji Sugimoto
Format: Article
Language:English
Published: SpringerOpen 2020-05-01
Series:Journal of High Energy Physics
Subjects:
Differential and Algebraic Geometry
Nonperturbative Effects
Topological Strings
Online Access:http://link.springer.com/article/10.1007/JHEP05(2020)026
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spelling doaj-9f5f632750ae4eff9ce1abfd3d1a5e382020-11-25T02:01:35ZengSpringerOpenJournal of High Energy Physics1029-84792020-05-012020511910.1007/JHEP05(2020)026Bloch electrons on honeycomb lattice and toric Calabi-Yau geometryYasuyuki Hatsuda0Yuji Sugimoto1Department of Physics, Rikkyo UniversityInterdisciplinary Center for Theoretical Study, University of Science and Technology of ChinaAbstract 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.http://link.springer.com/article/10.1007/JHEP05(2020)026Differential and Algebraic GeometryNonperturbative EffectsTopological Strings
collection DOAJ
language English
format Article
sources DOAJ
author Yasuyuki Hatsuda
Yuji Sugimoto
spellingShingle Yasuyuki Hatsuda
Yuji Sugimoto
Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry
Journal of High Energy Physics
Differential and Algebraic Geometry
Nonperturbative Effects
Topological Strings
author_facet Yasuyuki Hatsuda
Yuji Sugimoto
author_sort Yasuyuki Hatsuda
title Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry
title_short Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry
title_full Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry
title_fullStr Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry
title_full_unstemmed Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry
title_sort bloch electrons on honeycomb lattice and toric calabi-yau geometry
publisher SpringerOpen
series Journal of High Energy Physics
issn 1029-8479
publishDate 2020-05-01
description Abstract 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.
topic Differential and Algebraic Geometry
Nonperturbative Effects
Topological Strings
url http://link.springer.com/article/10.1007/JHEP05(2020)026
work_keys_str_mv AT yasuyukihatsuda blochelectronsonhoneycomblatticeandtoriccalabiyaugeometry
AT yujisugimoto blochelectronsonhoneycomblatticeandtoriccalabiyaugeometry
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