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The Quantum Group and Harper Equation on a Honeycomb Lattice

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Abstract

The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. The one-particle Hamiltonian is expressed in terms of the generators of the quantum group U q (sl 2). The corresponding Harper equation is rewritten as a system of two coupled functional equations in the complex plane. The system is shown to exhibit certain symmetry that allows one to resolve the entanglement, and the basic single equation determining the eigenvalues and eigenstates is obtained. Equations specifying the roots of eigenstates in the complex plane are found.

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References

  1. P. B. Wiegmann and A. V. Zabrodin, “Bethe-ansatz for the Bloch electron in magnetic field,” Phys. Rev. Lett., 72, No. 12, 1890–1893 (1994).

    Article  MATH  Google Scholar 

  2. L. D. Faddeev and R. M. Kashaev, “Generalized Bethe ansatz equations for Hofstadter problem,” Commun. Math. Phys., 169, No. 1, 181–191 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Kohmoto and A. Sedrakyan, “Hofstadter problem on the honeycomb and triangular lattices: Bethe ansatz solution,” Phys. Rev. B, 73, No. 23, 235118 (2006).

    Article  Google Scholar 

  4. M. Eliashvili, G. I. Japaridze, and G. Tsitsishvili, “The quantum group, Harper equation and structure of Bloch eigenstates on a honeycomb lattice,” J. Phys. A: Math. Theor., 45, No. 39, 395305 (2012).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    M. Eliashvili & G. Tsitsishvili

  2. A. Razmadze Mathematical Institute, Tbilisi, Georgia

    M. Eliashvili & G. Tsitsishvili

  3. Ilia State University, Tbilisi, Georgia

    G. Japaridze

Authors
  1. M. Eliashvili
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  2. G. Tsitsishvili
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  3. G. Japaridze
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Corresponding author

Correspondence to M. Eliashvili.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 94, Proceedings of the International Conference “Lie Groups, Differential Equations, and Geometry,” June 10–22, 2013, Batumi, Georgia, Part 1, 2014.

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Eliashvili, M., Tsitsishvili, G. & Japaridze, G. The Quantum Group and Harper Equation on a Honeycomb Lattice. J Math Sci 216, 522–526 (2016). https://doi.org/10.1007/s10958-016-2909-8

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  • DOI: https://doi.org/10.1007/s10958-016-2909-8

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