Luttinger Liquid with Attraction and One Impurity: Exact Solution

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Abstract

The exact solution to the problem of scattering of one-dimensional attracted fermions on a point impurity, which exists in the Kane–Fisher model is analyzed for a Luttinger parameter equal to 2. The expression obtained for the frequency dependence of the coefficient of fermion reflection from an impurity demonstrates impossibility of extrapolation of results for a relatively weak fermion–fermion interaction to the range of coupling constants on the order of unity.

About the authors

V. V Afonin

Ioffe Institute, Russian Academy of Sciences

Author for correspondence.
Email: vasili.afonin@mail.ioffe.ru
194021, St. Petersburg, Russia

References

  1. S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950).
  2. J. Schwinger, Phys. Rev. 128, 2425 (1962).
  3. G. S. Danilov, I. T. Dyatlov, and V. Yu. Petrov, Zh. Eksp. Theor. Fiz. 78, 1314 (1980)
  4. Sov. Phys. JETP 51, 663 (1980).
  5. C. L. Kane and M. P. A. Fisher, Phys. Rev. B 46, 15233 (1992).
  6. A. Furusaki and N. Nagaosa, Phys. Rev. B 47, 4631 (1993).
  7. L. I. Glazman, K. A. Matveev, and D. Yue, Phys. Rev. B 49, 1966 (1994).
  8. D. N. Aristov and P. W. W¨olfle, Phys. Rev. B 80, 045109 (2009).
  9. V. V. Afonin and V. Yu. Petrov, J. Phys.: Condens. Matter 30, 355601 (2018).
  10. A. Furusaki, Phys. Rev. B 56, 9352 (1997).
  11. P. Fendley, A.W.W. Ludwig, and H. Saleur, Phys. Rev. B 52, 8934 (1994).
  12. V. V. Afonin and V. Yu.Petrov, Pis'ma v ZhETF 97, 587 (2013).
  13. J. Bardeen, Phys. Rev. Lett. 6, 57 (1961).
  14. V. V. Afonin and V. Yu. Petrov, JETP Lett. 109, 762 (2019).
  15. Б. Л. Иоффе, УФН 178, 647 (2008).
  16. M. Peskin and D. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley (1996), pp. 654-656.
  17. V. V. Afonin and V. Yu. Petrov, JETP Lett. 101, 622 (2015).
  18. J. Hubbard, Phys. Rev. Lett. 3, 77 (1959).
  19. V. V. Afonin and S. V. Gantsevich, Cond. Mat. 4, 62 (2019); doi: 10.3390/condmat4030062.
  20. В. В. Афонин, В. Ю. Петров, ЖЭТФ 134, 637 (2008).
  21. F. D. M. Haldane, J. Phys. C 14, 2585 (1981).
  22. V. V. Afonin and V. Yu. Petrov, Found. Phys. 40, 190 (2010); doi: 10.1007/s10701-009-9385-7.
  23. H. Bateman and A. Erdelyi, Higher Transcendental Functions, Mc Graw-Hill Book Company, New York (1953), Vol. 2, p. 148.

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