Abstract
After a short review of the case for the t — J model as a suitable low energymodel Hamiltonian for CuO 2 planes in the high-Tc superconductors, the renormalized mean field approximation to this model is discussed. At half-filling the reduction to a Hilbert space containing only spin degrees of freedom leads to a wide class of degeneracies in the fermion meanfield description. One particular class of states which has generated much interest in the past year, is that built from one electron Hofstadter states which are eigenstates in the presence of a uniform magnetic flux. The mean field theory of such states in a t — J model is reviewed followed by a discussion of their unusual properties. In conclusion, some comments on the relationship to anyon models and other open questions are given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P.W. Anderson, Science 235, 1196 (1987) and in Proc. Int. School E. Fermi, Course CIV, eds. R.A. Broglia and J.R. Schrieffer, North Holland p. 1, 1987.
For an account of the magnetic properties see T.R. Thurston et al., Phys. Rev. B 40, 4585 (1989); K. Yamada et al., ibid. 4557; J.M. Tranquada et al., ibid 4503 and references therein.
F.C. Zhang and T.M. Rice, Phys. Rev. B 37, 3759 (1988).
M.S. Hybertsen, E.B. Stechel, M. Schlüter and D.R. Jennison, preprint.
See also A. Ramsak and P. Prelovsek, Phys. Rev. B 40, 2239 (1989); C.H. Chen, E.B. Schüttler and A.J. Fedro, preprint; W.H. Stephan, W. von der Linden and P. Horsch, Phys. Rev. B 39, 2924 (1989); M. Ogata and H. Shiba, preprint.
F. Mila, Phys. Rev. B 38 11358 (1988); A.K. Mc Mahon, R.M. Martin and S. Satpathy, Phys. Rev. B 38, 6650 (1989); H. Eskes and G.A. Sawatzky, Phys. Rev. Lett. 61, 1413 (1988).
H. Eskes, L.H. Tjeng and G.A. Sawatzky, Springer Series in Mater. Science, Vol. 11, 20 (1989).
F.C. Zhang, C. Gros, T.M. Rice and H. Shiba, Super. Sci. and Tech. 1, 36 (1988).
W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989); D. Vollhardt preprint, E. Müller-Hart mann preprint, M. Roos preprint.
G. Kotliar and A.E. Ruckenstein, Phys. Rev. Lett. 57, 1362 (1986).
P.W. Anderson in Ref. 1; I. Affleck, Z. Zou, T. Hsu and P.W. Anderson, Phys. Rev. B 38, 745 (1988).
I. Affleck and J.B. Marston, Phys. Rev. B 37, 3774 (1988); G. Kotliar, Phys. Rev. B 37, 3664 (1988).
C. Gros, Phys, Rev. B 38, 931 (1988).
see for example N. Trivedi and D.M. Ceperley, Phys. Rev. B 40, 2737 (1989) and preprint.
T.K. Lee and S. Feng, Phys. Rev. B 38, 11809 (1988).
Y. Hasegawa, P. Lederer, T.M. Rice and P. Wiegmann, Phys. Rev. Lett. 63, 907 (1989).
D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
G. Montambeaux, Phys. Rev. Lett. 63, 1657 (1989).
F. Nori, private communication.
P.W. Anderson, B.S. Shastry and D. Hristopolous, preprint.
P. Lederer, D. Poilblanc and T.M. Rice, Phys. Rev. Lett. 63, 1519 (1989).
S. Teitel and C. Jayaprakesh, Phys. Rev. Lett. 51, 1999 (1983); T.C. Halsey, Phys. Rev. B 31, 5728 (1985).
D. Poilblanc, Y. Hasegawa and T.M. Rice, preprint.
S. Liang and N. Trivedi, preprint.
A.B. Harris, T.C. Lubensky and F.J. Mele, Phys. Rev. B 40, 2631 (1989).
D. Poilblanc and Y. Hasegawa, preprint.
X.G. Wen, F. Wilczek and A. Zee, Phys. Rev. B 39, 11413 (1989); X.G. Wen and A. Zee, preprint.
B.I. Halperin and T.M. Rice, Solid State Phys. 21,115 (1968) (ed. F. Seitz, D. Turnbull and H. Ehrenreich, Acad. Press, N.Y.).
P. Lederer, D. Poilblanc and T.M. Rice, to be published.
P. Lederer and T.M. Rice, to be published.
V. Kalmeyer and R.B. Laughlin, Phys. Rev. Lett. 59, 2095 (1987). R.B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988) and Science 242, 525 (1988); P.B. Wiegmann, Phys. Rev. Lett. 60, 821 (1988).
Y.H. Chen, F. Wilczek, E. Witten and B.I. Halperin, preprint. A.L. Fetter, C.B. Hanna and R.B. Laughlin, Phys. Rev. B 39, 9679 (1989); G.S. Canright, S.M. Girvin and A. Brass, preprint.
B.I. Halperin, J. March-Russell and F. Wilczek, preprint.
F.C. Zhang, preprint.
G.M. Luke, private communication.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rice, T.M. (1990). Flux Phases in the t — J Model. In: Avishai, Y. (eds) Recent Progress in Many-Body Theories. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3798-4_1
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3798-4_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6693-5
Online ISBN: 978-1-4615-3798-4
eBook Packages: Springer Book Archive