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Upper Bounds on the Charge Susceptibility of Many-Electron Systems Coupled to the Quantized Radiation Field

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We extend the Kubo–Kishi theorem concerning the charge susceptibility of the Hubbard model in the following way: (i) The electron–photon interaction is taken into account. (ii) Not only on-site but also general Coulomb repulsions are considered.

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References

  1. Arai A.: Path integral representation of the index of Kahler-Dirac operators on an infinite-dimensional manifold. J. Funct. Anal. 82, 330–369 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Arai A.: Trace formulas, a Golden-Thompson inequality and classical limit in boson Fock space. J. Funct. Anal. 136, 510–547 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dollard, J.D., Friedman, C.N.: Product Integration with Application to Differential Equations. Encyclopedia of mathematics and its applications, vol. 10, 1979, Addison-Wesley Publishing Company

  4. Dyson F.J., Lieb E.H., Simon B.: Phase transitions in quantum spin systems with isotropic and nonisotropic interactions. J. Stat. Phys. 18, 335–383 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  5. Giuliani A., Mastropietro V., Porta M.: Lattice quantum electrodynamics for graphene. Ann. Phys. 327, 461–511 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Giuliani A., Mastropietro V., Porta M.: Universality of conductivity in interacting graphene. Commun. Math. Phys. 311, 317–355 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Gross L.: On the formula of Mathews and Salam. J. Funct. Anal. 25, 162–209 (1977)

    Article  Google Scholar 

  8. Gutzwiller M.: Effect of correlation on the ferromagnetism of transition metals. Phys. Rev. Lett. 10, 159–162 (1963)

    Article  ADS  Google Scholar 

  9. Hoegh-Krohn R.: Relativistic quantum statistical mechanics in two-dimensional space-time. Commun. Math. Phys. 38, 195–224 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  10. Hubbard J.: Electron correlation in narrow energy bands. Proc. Roy. Soc. (Lond.) A 276, 238–257 (1963)

    Article  ADS  Google Scholar 

  11. Kanamori J.: Electron correlation and ferromagnetism of transition metals. Prog. Theor. Phys. 30, 275–289 (1963)

    Article  ADS  Google Scholar 

  12. Kubo K., Kishi T.: Rigorous bounds on the susceptibilities of the Hubbard model. Phys. Rev. B 41, 4866–4868 (1990)

    Article  ADS  Google Scholar 

  13. Lieb E.H.: Two theorems on the Hubbard model. Phys. Rev. Lett. 62, 1201–1204 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  14. Lieb E.H.: Flux phase of the half-filled band. Phys. Rev. Lett. 73, 2158–2161 (1994)

    Article  ADS  Google Scholar 

  15. Lorinczi, J., Hiroshima, F., Betz, V.: Feynman-Kac-Type Theorems And Gibbs Measures On Path Space. With Applications To Rigorous Quantum Field Theory. de Gruyter Studies in Mathematics, vol. 34. Walter de Gruyter Co., Berlin (2011)

  16. Miyao T.: Ground state properties of the SSH model. J. Stat. Phys. 149, 519–550 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  17. Miyao, T.: Some rigorous results on the Holstein-Hubbard model, arXiv:1402.5202

  18. Nagaoka Y.: Ferromagnetism in a narrow, almost half-filled s band. Phys. Rev. 147, 392–405 (1966)

    Article  ADS  Google Scholar 

  19. Simon, B.: Trace Ideals and their Applications, 2nd edn. Mathematical Surveys and Monographs, vol. 120. American Mathematical Society, Providence, RI (2005)

  20. Tasaki H.: From Nagaoka’s ferromagnetism to flat-band ferromagnetism and beyond : an introduction to ferromagnetism in the Hubbard model. Progr. Theor. Phys. 99, 489–548 (1998)

    Article  ADS  Google Scholar 

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Miyao, T. Upper Bounds on the Charge Susceptibility of Many-Electron Systems Coupled to the Quantized Radiation Field. Lett Math Phys 105, 1119–1133 (2015). https://doi.org/10.1007/s11005-015-0775-9

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  • DOI: https://doi.org/10.1007/s11005-015-0775-9

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