Abstract
One-dimensional (1D) quantum models with 1/r 2 interaction have been studied extensively in connection with basic concepts in condensed matter physics such as the random matrix, the fractional quantum Hall effect (FQHE), etc [1–13]. Besides much interest in the integrability, the above class of quantum models involve interesting applications to highly correlated electron systems. The asymptotic Bethe ansatz solution (ABA) provides us with a systematic way to treat bulk quantities as well as excitation spectra [2]. We have obtained the ABA solution systematically to hierarchical families of quantum models with 1/r 2 interaction, such as the SU(N) Haldane-Shastry spin chain [8], the OSp(N, 1) supersymmetric t-J model [8], a new hierarchy related to the edge states of the FQHE with the filling fraction v = 1/(p 1 − 1/ p2 −…− 1/ pN ) [13].
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References
F. Calogero, J. Math. Phys. 10 (1969) 2197.
B. Sutherland, Phys. Rev. A4, 2019 (1971); A5, 1372 (1971).
F. D. M. Haidane, Phys. Rev. Lett. 60, 635 (1988); 66, 1529 (1991).
B. S. Shastry, Phys. Rev. Lett. 60, 639 (1988); 69, 164 (1992).
Y. Kuramoto and H. Yokoyama, Phys. Rev. Lett. 67, 1338 (1991).
N. Kawakami and S.-K. Yang, Phys. Rev. Lett. 67, 2493 (1991).
F. D. M. Haldane, Z. N. C. Ha, J. C. Telstra, D. Bernard, and V. Pasquier, Phys. Rev. Lett. 69 2021 (1992).
N. Kawakami, Phys. Rev. B46, 1005, 3192 (1992).
Z. N. C. Ha and F. D. M. Haldane, Phys. Rev. B46, 9359 (1992).
A. P. Polychronakos, Phys. Rev. Lett. 69, 703 (1992).
K. Hikami and M. Wadati, J. Phys. Soc. Jpn. 62, 469 (1993).
B. S. Shastry and B. Sutherland, Phys. Rev. Lett. 70, 4029 (1993)
B. Sutherland and B. S. Shastry, Phys. Rev. Lett. 71, 5 (1993).
N. Kawakami, Phys. Rev. Lett. 71, 275 (1993); J. Phys. Soc. Jpn. 62, No.12 (1993).
N. Kawakami, Kyoto preprint YITP/K-1013 (April, 1993)
K. Vacek, A. Okiji and N. Kawakami, J. Phys. Soc. Jpn. 62, 3818 (1993); Phys. Rev. B. to be published.
N. Kawakami, J. Phys. Soc. Jpn. 62, 2270, 2419 (1993).
P. B. Wiegmann, Phys. Rev. Lett. 60, 821 (1988).
B. Sutherland, Phys. Rev. B 12 (1975) 3795.
A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, Nucl. Phys. B241 (1984) 333.
H. J. de Vega, J. Phys. A21 (1988) L1089; J. Suzuki, J. Phys. A21 (1988) L1175.
H. Frahm and V. E. Korepin, Phys. Rev. B 42, 10553 (1990).
R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983)
B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984)
J. K. Jain, Phys. Rev. Lett. 63, 199 (1989).
B. Blok and X. G. Wen, Phys. Rev. B42, 8133 (1990)
N. Read, Phys. Rev. Lett. 65, 1502 (1990).
X. G. Wen, Phys. Rev. Lett. 64, 2206 (1990); Phys. Rev. B41, 12838 (1990).
J. H. F. Scott-Thomas et al., Phys. Rev. Lettt. 62, 583 (1989)
U. Meirav et al., Phys. Rev. B40, 5871 (1989)
U. Meirav et al., Phys. Rev. Lett. 65, 771 (1990).
H. van Houten and C. W. J. Beenakker, Phys. Rev. Lett. 63, 1893 (1989)
Y. Meir, N. S. Wingreen, and P. A. Lee, ibid. 66, 3048 (1991).
S. Tewari, Phys. Rev. B46, 7782 (1992).
N. F. Johnson and M. C. Payne, Phys. Rev. Lett. 70, 1513 (1993).
J. Minahan and A. P. Polychronakos, Phys. Lett. B302, 265 (1993)
see also H. Frahm, J. Phys. A26, L473 (1993).
K. Vacek, A. Okiji and N. Kawakami, preprint.
N. Kawakami and Y. Kuramoto, preprint.
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Kawakami, N. (1995). Hierarchy of 1D Electron Models with Long-Range Interaction. In: Baeriswyl, D., Campbell, D.K., Carmelo, J.M.P., Guinea, F., Louis, E. (eds) The Hubbard Model. NATO ASI Series, vol 343. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1042-4_4
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