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spin ≈ 0.5J that carries most of the weight (9, 14).
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1 using numerical techniques.
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(preprint) recently presented magnetic susceptibility measurements for Zn-doped 2- and 3-leg ladders
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M. Azuma, M Takano, T. Ishida, and K. Okuda (preprint) recently presented magnetic susceptibility measurements for Zn-doped 2- and 3-leg ladders.
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4243127827
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7, it is not clear whether the t - J model is suitable for describing its properties upon doping. A detailed analysis based on a manyorbital Hubbard model for V and O ions is needed.
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Calculations of superconducting correlations for the Hubbard model were discussed in (12) and also in Y. Asai, Phys. Rev. B 50, 6519 (1994), and preprint;
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c superconductors where the infrared Drude weight scales as the hole concentration, whereas the Fermi surface is large and electron-like (10). 50. Numerical studies in odd-leg ladders beyond the single chain have not been explicitly carried out. However, the discussion linking the spin gap with hole-pair formation suggests that the tendency to superconduct in the odd-leg ladders is weaker than in the even-leg ladders. The issue of superconductivity in the 2D limit, reached when the width of the ladders increases, is subtle and is not addressed here.
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67
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4243159421
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Univ. of Tokyo preprint
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Several recent publications have addressed these issues: N. Nagaosa (Univ. of Tokyo preprint) claimed that the low-energy physics of doped ladders is described in terms of bipolarons; L. Balents and M. P. A. Fisher (ITP preprint), studying the Hubbard model ladder with a controlled RG method, found a phase with a finite spin gap and a single gapless charge mode that they interpret as the analog of a 1D superconductor or a charge density wave; and H. J. Schulz (Orsay preprint) studied two coupled Luttinger liquids, reporting a spin gap in the spectrum and either d-type pairing or orbital AF fluctuations in the ground state. The addition of a long-range Coulomb force to the t - J model leads to a competition between superconductivity and charge-density wave states [see U. Lòw, V. J. Emery, K. Fabricius, S. A. Kivelson, Phys. Rev. Lett. 72, 1918 (1994); S. Haas, E Dagotto, A. Nazarenko, J. Riera, Phys. Rev. B 51, 5989 (1995)].
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68
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4243070443
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ITP preprint
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Several recent publications have addressed these issues: N. Nagaosa (Univ. of Tokyo preprint) claimed that the low-energy physics of doped ladders is described in terms of bipolarons; L. Balents and M. P. A. Fisher (ITP preprint), studying the Hubbard model ladder with a controlled RG method, found a phase with a finite spin gap and a single gapless charge mode that they interpret as the analog of a 1D superconductor or a charge density wave; and H. J. Schulz (Orsay preprint) studied two coupled Luttinger liquids, reporting a spin gap in the spectrum and either d-type pairing or orbital AF fluctuations in the ground state. The addition of a long-range Coulomb force to the t - J model leads to a competition between superconductivity and charge-density wave states [see U. Lòw, V. J. Emery, K. Fabricius, S. A. Kivelson, Phys. Rev. Lett. 72, 1918 (1994); S. Haas, E Dagotto, A. Nazarenko, J. Riera, Phys. Rev. B 51, 5989 (1995)].
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Balents, L.1
Fisher, M.P.A.2
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69
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4243079450
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Orsay preprint
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Several recent publications have addressed these issues: N. Nagaosa (Univ. of Tokyo preprint) claimed that the low-energy physics of doped ladders is described in terms of bipolarons; L. Balents and M. P. A. Fisher (ITP preprint), studying the Hubbard model ladder with a controlled RG method, found a phase with a finite spin gap and a single gapless charge mode that they interpret as the analog of a 1D superconductor or a charge density wave; and H. J. Schulz (Orsay preprint) studied two coupled Luttinger liquids, reporting a spin gap in the spectrum and either d-type pairing or orbital AF fluctuations in the ground state. The addition of a long-range Coulomb force to the t - J model leads to a competition between superconductivity and charge-density wave states [see U. Lòw, V. J. Emery, K. Fabricius, S. A. Kivelson, Phys. Rev. Lett. 72, 1918 (1994); S. Haas, E Dagotto, A. Nazarenko, J. Riera, Phys. Rev. B 51, 5989 (1995)].
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70
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Several recent publications have addressed these issues: N. Nagaosa (Univ. of Tokyo preprint) claimed that the low-energy physics of doped ladders is described in terms of bipolarons; L. Balents and M. P. A. Fisher (ITP preprint), studying the Hubbard model ladder with a controlled RG method, found a phase with a finite spin gap and a single gapless charge mode that they interpret as the analog of a 1D superconductor or a charge density wave; and H. J. Schulz (Orsay preprint) studied two coupled Luttinger liquids, reporting a spin gap in the spectrum and either d-type pairing or orbital AF fluctuations in the ground state. The addition of a long-range Coulomb force to the t - J model leads to a competition between superconductivity and charge-density wave states [see U. Lòw, V. J. Emery, K. Fabricius, S. A. Kivelson, Phys. Rev. Lett. 72, 1918 (1994); S. Haas, E Dagotto, A. Nazarenko, J. Riera, Phys. Rev. B 51, 5989 (1995)].
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25944431981
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Several recent publications have addressed these issues: N. Nagaosa (Univ. of Tokyo preprint) claimed that the low-energy physics of doped ladders is described in terms of bipolarons; L. Balents and M. P. A. Fisher (ITP preprint), studying the Hubbard model ladder with a controlled RG method, found a phase with a finite spin gap and a single gapless charge mode that they interpret as the analog of a 1D superconductor or a charge density wave; and H. J. Schulz (Orsay preprint) studied two coupled Luttinger liquids, reporting a spin gap in the spectrum and either d-type pairing or orbital AF fluctuations in the ground state. The addition of a long-range Coulomb force to the t - J model leads to a competition between superconductivity and charge-density wave states [see U. Lòw, V. J. Emery, K. Fabricius, S. A. Kivelson, Phys. Rev. Lett. 72, 1918 (1994); S. Haas, E Dagotto, A. Nazarenko, J. Riera, Phys. Rev. B 51, 5989 (1995)].
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note
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We thank M. Azuma, T. Bames, V J. Emery, H. Hiroi, A. Moreo, J. Riera, D. J Scalapino, M. Takano, M. Troyer, and H Tsunetsugu for their help in the preparation of this review. E D. specially thanks the Office of Naval Research for its support under grant ONR N00014-93-0495. He also thanks the National High Magnetic Field Laboratory and the Center for Materials Research and Technology (MARTECH) for additional support.
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