Abstract
We propose a Green's function technique, to investigate finite-temperature properties of the Hubbard model on the triangular lattice. The lattices are covered by dimers. The method is exact in two limits:U=0 or decoupled dimers. We apply this approximate method to calculate the ground state energy, the specific heat and the single-particle spectral weight for the 1/2-filled case. The largest lattice considered has 16×16 sites. The approximate ground state energy as a function of the on-site interactionU oscillates around the exact energyin the 1/2-filled case. We find two peaks in the specific heat. ForU≥5t the single-particle spectral weight splits into upper and lower Hubbard bandasymmetrically. Thus in the 1/2-filled case the chemical potential is placed in the upper band leading to a metallic state. The approximate technique yields a finite zero-point entropy for mediumU. All the investigations signal a RVB state in the range of mediumU as formerly proposed by Callaway.
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References
Fukamachi, K., Nishimori, H.: Phys. Rev. B49, 651 (1994)
Röder, H.: Private communication 1994
Wannier, C.H.: Phys. Rev.79, 357 (1950)
Lorenz, B.: Phys. Status Solid: (b)119, 555 (1983)
Anderson, P.W.: Mater. Res. Bull.8, 153 (1973)
Fazekas, P., Anderson, P.W.: Philos. Mag.30, 423 (1974)
Kalmeyer, V., Laughlin, R.B.: Phys. Rev. Lett.59, 2095 (1987)
Huse, D.A., Elser, V.: Phys. Rev. Lett.60, 2531 (1988)
Jolicoeur, T., Guillou, J.C. Le: Phys. Rev. B40, 2727 (1989)
Bernu, B., Lhuillier, C., Pierre, L.: Phys. Rev. Lett.69, 2590 (1992)
Leung, P.W., Runge, K.J.: Phys. Rev. B47, 5861 (1993)
Bernu, B., Lecheminant, P., Lhuillier, C., Pierre, L: Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice. Preprint 1994
Singh, R.R.P., Huse, D.A.: Phys. Rev. Lett.68, 1766 (1992)
Chen, Y.-C.: Optimizing the RVB state on a triangular lattice: presence of the long-range order. Mod. Phys. Lett. B8, 1253 (1994)
Anderson, P.W.: Phys. Rev.115, 2 (1959)
Takahashi, M.: J. Phys. C10, 1289 (1977)
MacDonald, A.H., Girvin, S.M., Yoshioka, D.: Phys. Rev. B37, 9753 (1988)
MacDonald, A.H., Girvin, S.M., Yoshioka, D.: Phys. Rev.41, 2565 (1990)
Callaway, J.: Phys. Rev. B35, 8723 (1987)
Mistriotis, A., Büttner, H., Pesch, W.: J. Phys. C21, L1021 (1988)
Kato, M, Kokubo, F.: Phys. Rev. B49, 8864 (1994)
Pauling, L.: J. Chem. Phys.1, 280 (1933)
Pauling, L.: Proc. N. A. S.39, 551 (1953)
Mazumdar, S., Soos, Z.G.: Synth. Metals1, 77 (1979)
Anderson, P.W.: Science235, 1196 (1987)
Kohn, W.: Phys. Rev.133, A 171 (1964)
Côté, R., Tremblay, A.-M.S.: Spiral magnets as gapless MOTT insulators. Preprint 1994
Gazza, C.J., Trumper, A.E., Ceccatto, H.A.: J. Phys. C6, L625 (1994)
Kaplan, T.A.: Nuclear Physics B [Proc.Suppl.]5 A, 151 (1988)
Kaplan, T.A.: J. Appl. Phys.63, 4226 (1988)
Sutherland, B.: Phys. Rev. B37, 3786 (1988)
Liang, S., Doucot, B., Anderson, P.W.: Phys. Rev. Lett.61, 365 (1988)
Majumdar, C.K., Ghosh, D.K.: J. Math. Phys.10, 1388 (1969)
Tonegawa, T., Harada, I.: J. Phys. Soc. Jpn.56, 2153 (1987)
White, S.R., Noack, R.M., Scalapino, D.J.: Phys. Rev. Lett.73, 886 (1994)
Liebmann, R., Statistical mechanics of periodic frustrated Ising systems. Lecture Notes in Physics Vol. 251. Berlin Heidelberg, New York: Springer 1986
Caspers, W.: Spin systems. Singapore, New Jersey, London, Hong Kong: World Scientific 1989
Bonesteel, N.E.: Phys. Rev. B40, 8954 (1989)
Krivoshey, I.V.: Low Temp. Phys.20, 321 (1994)
Elk, K., Gasser, W.: Die Methode der Greenschen Funktionen in der Festkörperphysik. Berlin: Akademie-Verlag 1979
Mahan, G.D.: Many-particle particle physics. New York, London: Plenum Press 1990
Jänich, K.: Analysis für Physiker und Ingenieure. Berlin, Heidelberg, New York: Springer 1983
Engeln-Muellges, G., Reutter, F.: Formelsammlung zur numerischen Mathematik mit Standard-FORTRAN 77 Programmen. Mannheim, Wien, Zürich: Bibliographisches Institut 1986
Fano, G., Ortolani, F.: Phys. Rev. B42, 6877 (1990)
Waas, V.: Exact Lanczos diagonalization studies. Private communication 1992
Moreo, A.: Phys. Rev. B48, 3380 (1993)
Silver, R.N., Röder, H.: Densities of states of megadimensional Hamiltonian matrices. Preprint 1994
Cabib, D., Kaplan, T.A.: Phys. Rev. B7, 2199 (1973)
Matsuyama, H., Takahashi, T., Okabe, Y., Katayama-Yoshida, H., Kashiwakura, T., Sato, S., Kosugi, N., Yagishita, A., Tanaka, K., Fujimoto, H., Inokuchi, H.: Physica C160, 567 (1989)
Allen, J.W., Olson, C.G., Maple, M.B., Kang, J.-S., Liu, L.Z., Park, J.-H., Anderson, R.O., Ellis, W.P., Markert, J.T., Dalichaouch, Y., Liu, R.: Phys. Rev. Lett.64, 595 (1990)
Campuzano, J.C., Jennings, G., Faiz, M., Beaulaigue, L., Veal, B.W., Liu, J.Z., Paulikas, A.P., Vandervoort, K., Claus, H.: Phys. Rev. Lett.64, 2308 (1990)
Shen, Z.-X., Shih, C.K., Jepsen, O., Spicer, W.E., Lindau, I., Allen, J.W.: Phys. Rev. Lett.64, 2442 (1990)
Takahashi, T., Matsuyama, H., Katayama-Yoshida, H., Seki, K., Kamiya, K., Inokuchi, H.: Physica C170, 416 (1990)
Watanabe, T., Takahashi, T., Suzuki, S., Sato, S., Katayama-Yoshida, H.: Phys. Rev. B44, 5316 (1991)
Tan, L., Li, Q., Callaway, J.: Phys. Rev. B44, 341 (1991)
Jayaprakash, C., Krishnamurthy, H.R., Sarker, S., Wenz, W.: Europhys. Lett.15, 625 (1991)
Bogolyubov, N.N., Moskalenko, V.A.: Theor. Mat. Phys. (USA)86, 10 (1991)
Dagotto, E., Moreo, A., Ortolani, F., Scalapino, D.J.: Phys. Rev. B45, 10107 (1992)
Kasteleyn, P.W.: J. Math. Phys.4, 287 (1963)
Hayn, R., Plechko, V.N.: J. Phys. A27, 4753 (1994)
Pesch, W., Büttner, H., Reichl, J.: Phys. Rev. B37, 5887 (1988)