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Nagaoka’s Theorem in the Holstein–Hubbard Model

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Abstract

Nagaoka’s theorem on ferromagnetism in the Hubbard model is extended to the Holstein–Hubbard model. This shows that Nagaoka’s ferromagnetism is stable even if the electron–phonon interaction is taken into account. We also prove that Nagaoka’s ferromagnetism is stable under the influence of the quantized radiation field.

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Acknowledgements

This work was partially supported by KAKENHI (20554421) and KAKENHI(16H03942). I would be grateful to the anonymous referee for useful comments.

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Authors and Affiliations

  1. Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

    Tadahiro Miyao

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  1. Tadahiro Miyao
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Correspondence to Tadahiro Miyao.

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Communicated by Vieri Mastropietro.

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Miyao, T. Nagaoka’s Theorem in the Holstein–Hubbard Model. Ann. Henri Poincaré 18, 2849–2871 (2017). https://doi.org/10.1007/s00023-017-0584-z

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