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Generic Features of an Electron Injected into the Luttinger Liquid

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Abstract

An extra electron injected into the Luttinger liquid (LL) is not completely separated into spin and charge excitations, but it provides a peak of an electron-like excitation in addition to the two prominent spin- and charge-excitation peaks in the one-electron spectral function of an interacting one-dimensional (1D) system. By a scaling argument based on a renormalization-group scheme, we obtain universal features of this electron-like excitation for low energies and in the vicinity of the Fermi point, which are entirely characterized by the Luttinger parameter K c and the renormalized Fermi velocity v F at the LL fixed point. The latter quantity v F is shown to be given by the slope of the lowest excitation spectrum near the Fermi point in the system with large but finite size. Some of exact results are presented for the 1D Hubbard model at n=0.59 filling.

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References

  1. Tomonaga, S.: Prog. Theor. Phys. 5, 544 (1950)

    Article  ADS  MathSciNet  Google Scholar 

  2. Luttinger, J.M.: J. Math. Phys. 4, 1154 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  3. Haldane, F.D.M.: J. Phys. C 14, 2585 (1981)

    Article  ADS  Google Scholar 

  4. Meden, V., Schönhammer, K.: Phys. Rev. B 46, 15753 (1992)

    Article  ADS  Google Scholar 

  5. Voit, J.: Phys. Rev. B 47, 6740 (1993)

    Article  ADS  Google Scholar 

  6. Orignac, E., Tsuchiizu, M., Suzumura, Y.: Phys. Rev. B 84, 165128 (2011)

    Article  ADS  Google Scholar 

  7. Voit, J.: J. Phys.: Condens. Matter 5, 8305 (1993)

    ADS  Google Scholar 

  8. Maebashi, H., Takada, Y.: Phys. Rev. B 89, 201109(R) (2014)

    Article  ADS  Google Scholar 

  9. For studies beyond the Luttinger liquid theory, see A. Imambekov, T. L. Schmidt, and L. I. Glazman, Rev. Mod. Phys. 84 1253 (2012)

  10. Claessen, R., et al.: Phys. Rev. Lett. 88, 096402 (2002)

    Article  ADS  Google Scholar 

  11. Sing, M., et al.: Phys. Rev. B 68, 125111 (2003)

    Article  ADS  Google Scholar 

  12. Benthien, H., Gebhard, F., Jeckelmann, E.: Phys. Rev. Lett. 92, 256401 (2004)

    Article  ADS  Google Scholar 

  13. Carmelo, J.M.P., et al.: J. Phys.: Condens. Matter 18, 5191 (2006)

    ADS  Google Scholar 

  14. Carmelo, J.M.P., Bozi, D., Penc, K.: J. Phys.: Condens. Matter 20, 415103 (2008)

    Google Scholar 

  15. Essler, F.H.L.: Phys. Rev. B 81, 205120 (2010)

    Article  ADS  Google Scholar 

  16. Shankar, R.: Rev. Mod. Phys. 66, 129 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  17. Metzner, W., Castellani, C., Castro, C.D.: Adv. Phys. 47, 317 (1998)

    Article  ADS  Google Scholar 

  18. Sólyom, J.: Fundamentals of the Physics of Solids, vol. 3. Springer, Berlin, Heidelberg (2010)

    Google Scholar 

  19. Woynarovich, F.: J. Phys. A 22, 4243 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  20. Sólyom, J.: Adv. Phys. 28, 201 (1979)

    Article  ADS  Google Scholar 

  21. Suzumura, Y.: Prog. Theor. Phys. 63, 51 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  22. Schönhammer, K., Meden, V.: Phys. Rev. B 47, 16205 (1993) ; 48, 11390 (1993)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work is partially supported by Innovative Area “Materials Design through Computics: Complex Correlation and Non-Equilibrium Dynamics” (No. 22104011) from MEXT, Japan.

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Authors and Affiliations

  1. Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba, 277-8581, Japan

    Hideaki Maebashi & Yasutami Takada

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  1. Hideaki Maebashi
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  2. Yasutami Takada
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Correspondence to Hideaki Maebashi.

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Maebashi, H., Takada, Y. Generic Features of an Electron Injected into the Luttinger Liquid. J Supercond Nov Magn 28, 1331–1335 (2015). https://doi.org/10.1007/s10948-014-2914-4

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  • DOI: https://doi.org/10.1007/s10948-014-2914-4

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