Luttinger liquids with boundaries: Power-laws and energy scales

European Physical Journal B

Volumn 16, Issue 4, 2000, Pages 631-646

  Meden, V ^a,b   Metzner, W ^a   Schollwock U ^c   Schneider, O ^a   Stauber, T ^b   Schonhammer K ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

^c UNIVERSITY OF MUNICH   (Germany)

Author keywords

71.10. w theories and models of many electron systems; 71.10.Pm fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)

Indexed keywords

EID: 0001525511     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510070180     Document Type: Article

References (39)

1. For a review see: J. Voit, Rep. Prog. Phys. 58, 977 (1995)
2. S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950).
3. J.M. Luttinger, J. Math. Phys. 4, 1154 (1963).
4. D.C. Mattis, E.H. Lieb, J. Math. Phys. 6, 304 (1965).
5. J. Sólyom, Adv. Phys. 28, 201 (1979).
6. F.D.M. Haldane, J. Phys. C 14, 2585 (1981).
7. H.J. Schulz, Phys. Rev. Lett. 64, 2831 (1990).
8. S. Qin et al., Phys. Rev. B 56, 9766 (1997).
9. D.C. Mattis, J. Math. Phys. 15, 609 (1974).
10. C.L. Kane, M.P.A. Fisher, Phys. Rev. Lett. 68, 1220 (1992)
11. M. Fabrizio, A. Gogolin, Phys. Rev. B 51, 17827 (1995).
12. S. Eggert, H. Johannesson, A. Mattsson, Phys. Rev. Lett. 76, 1505 (1996).
13. Y. Wang, J. Voit, F.-C. Pu, Phys. Rev. B 54, 8491 (1996).
14. J. Voit, Y. Wang, M. Grioni, Phys. Rev. B 61, 7930 (2000).
15. G. Bedürftig et al., Phys. Rev. B 58, 10225 (1998).
16. Introductions to bosonization are given in K. Schönhammer, cond-mat/9710330; J. von Delft, H. Schoeller, Ann. Phys. 7, 225 (1998).
17. Introductions to bosonization are given in K. Schönhammer, cond-mat/9710330; J. von Delft, H. Schoeller, Ann. Phys. 7, 225 (1998).
18. Without presenting a derivation the difference between the boundary and bulk exponent was already pointed out in reference [10].
19. Density-Matrix Renormalization, edited by I. Peschel et al. (Springer, Berlin, 1999) and references therein.
20. R. Preuss et al., Phys. Rev. Lett. 73, 732 (1994).
21. For a recent review of the experimental situation see: M. Grioni, J. Voit, in Electron spectroscopies applied to low-dimensional materials, edited by H. Stanberg, H. Hughes (1999).
22. F. Zwick et al., Phys. Rev. Lett. 79, 3982 (1997).
23. J.D. Denlinger et al., Phys. Rev. Lett. 82, 2540 (1999).
24. J. Xue et al., Phys. Rev. Lett. 83, 1235 (1999).
25. P. Segovia et al., Nature 402, 504 (1999).
26. Here we only consider the case of an equal number of electrons with up and down spin.
27. T. Stauber, Diploma-thesis, Universität Göttingen, 1998.
28. As the Green's and spectral function are independent of the spin direction s we have suppressed the spin index.
29. Here we neglect all the problems which might occur due to local minima and maxima in ξ(k) or bandedges.
30. K. Schönhammer, V. Meden, Phys. Rev. B 47, 16205 (1993).
31. K. Schönhammer, V. Meden, W. Metzner, U. Schollwöck, O. Gunnarsson, Phys. Rev. B 61, 4393 (2000).
32. HF.
33. M. Klaus, J. Math. Phys. 32, 163 (1991).
34. ρ = 1 - U/(2πvπ). Note the misprint in equation (8) of reference [7].
35. G. Schliecker et al., J. Phys. Cond. Matter 7, 7969 (1995).
36. J.R. Taylor, Scattering Theory (Wiley, New York, 1972).
37. ω̃(j) in equation (6.22) has been replaced by 1.
38. P. Kopietz, V. Meden, K. Schönhammer, Phys. Rev. Lett. 74, 2997 (1995); E. Arrigoni, Phys. Rev. Lett. 83, 128 (1999).
39. P. Kopietz, V. Meden, K. Schönhammer, Phys. Rev. Lett. 74, 2997 (1995); E. Arrigoni, Phys. Rev. Lett. 83, 128 (1999).