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K. Kanoda: Physica C 282-287 (1997) 299;
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0001326296
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Williams, J.M.6
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Arai, T.1
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Yamada, J.5
Nakatsuji, S.6
Anzai, H.7
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17
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33847394875
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In this paper, we use the term Mott transition for a transition from a conductive state to a nonmagnetic insulating state. Thus, we discriminate it from a magnetic transition like a metal-to-AF-insulator transition
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In this paper, we use the term "Mott transition" for a transition from a conductive state to a nonmagnetic insulating state. Thus, we discriminate it from a magnetic transition like a metal-to-AF-insulator transition.
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27
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0001328394
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M. Tamura, H. Tajima, K. Yakushi, H. Kuroda, A. Kobayashi, R. Kato and H. Kobayashi: J. Phys. Soc. Jpn. 60 (1991) 3861.
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J. Phys. Soc. Jpn
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Tamura, M.1
Tajima, H.2
Yakushi, K.3
Kuroda, H.4
Kobayashi, A.5
Kato, R.6
Kobayashi, H.7
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28
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33847380565
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At half filling, the results for t′ (< 0) are identical to those for |t′, We hence concentrate on the case of t′/t ≥ 0
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At half filling, the results for t′ (< 0) are identical to those for |t′|. We hence concentrate on the case of t′/t ≥ 0.
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36
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33847401380
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Because the t-J and Hubbard models are related in the strong coupling regime through a canonical transformation, ℋt-J ≈ eiSℋHube-iS,36 in which S is given as Σ〈ij〉σ -it/U [ni-σ(1-n j-σ)ciσ† cjσ(1-ni-σ) ciσ†cjσ] the expectation values of the t-J model with respect to ΨG are approximately equivalent to those of the Hubbard model with respect to e-iSΨG. When one expands e -iS, the first-order part (∼t/U) of e -iSΨG broadly corresponds to ℘QΨG. Thus, the favorable fe
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QΨG.
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43
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33847391527
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It is difficult to estimate proper values of Z as a function of U/t with a finite-sized system, in the case that the position of the quasi-Fermi point moves and crosses a k point, when U/t is varied. As an example, we show the case of t′/t = 0.4 and L = 12 in Fig. 6, where the data for U/t = 6.5 deviates to some extent. For this parameter set, we find the quasi-Fermi point to shift in the nodal direction in Fig. 5(a).
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It is difficult to estimate proper values of Z as a function of U/t with a finite-sized system, in the case that the position of the quasi-Fermi point moves and crosses a k point, when U/t is varied. As an example, we show the case of t′/t = 0.4 and L = 12 in Fig. 6, where the data for U/t = 6.5 deviates to some extent. For this parameter set, we find the quasi-Fermi point to shift in the nodal direction in Fig. 5(a).
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46
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33847381026
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Generally, as system size decreases, the critical behavior near a phase transition tends to be less sharp, because a transition, in a strict sense, takes place only for Ns → ∞. For instance, the curve for t′, 0 and L, 10 in Fig. 8 (open square) is relatively smooth, whereas the curve for L, 16 seems to have an obvious jump. Thus, one must necessarily check system-size dependence to treat a phase transition
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s → ∞. For instance, the curve for t′ = 0 and L = 10 in Fig. 8 (open square) is relatively smooth, whereas the curve for L = 16 seems to have an obvious jump. Thus, one must necessarily check system-size dependence to treat a phase transition.
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57
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For instance
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For instance, M. Imada: Phys. Rev. B 72 (2005) 075113.
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Phys. Rev. B
, vol.72
, pp. 075113
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Imada, M.1
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We adopt the Manhattan metric to measure |R| and |r|.
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We adopt the Manhattan metric to measure |R| and |r|.
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59
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33847386210
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d(r) in eq. (17) is useful, because we are interested in the SC arising, particularly, near the Mott transition.
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d(r) in eq. (17) is useful, because we are interested in the SC arising, particularly, near the Mott transition.
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60
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33847391964
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c for t′/t = 0.7 and 0.8.
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c for t′/t = 0.7 and 0.8.
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62
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25644451991
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T. Watanabe, H. Yokoyama, Y. Tanaka, J. Inoue and M. Ogata: Physica C 426-431 (2005) 289.
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Physica C
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Watanabe, T.1
Yokoyama, H.2
Tanaka, Y.3
Inoue, J.4
Ogata, M.5
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64
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Y. Kurosaki, Y. Shimizu, K. Miyagawa, K. Kanoda and G. Saito: Phys. Rev. Lett. 95 (2005) 177001.
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Phys. Rev. Lett
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Kurosaki, Y.1
Shimizu, Y.2
Miyagawa, K.3
Kanoda, K.4
Saito, G.5
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65
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0031327963
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This feature is similar to that in the inorganic spin-Peierls compound CuGeO3, in which the value of J′/J drastically varies (including sign) under pressure. See, e.g, H. Yokoyama and Y. Saiga: J. Phys. Soc. Jpn. 66 (1997) 3617;
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3, in which the value of J′/J drastically varies (including sign) under pressure. See, e.g., H. Yokoyama and Y. Saiga: J. Phys. Soc. Jpn. 66 (1997) 3617;
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67
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M. Rahal, D. Chasseau, J. Gaultier, L. Ducasse, M. Kurmoo and P. Day: Acta Crystallogr., Sect. B 53 (1997) 159.
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Acta Crystallogr., Sect. B
, vol.53
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Rahal, M.1
Chasseau, D.2
Gaultier, J.3
Ducasse, L.4
Kurmoo, M.5
Day, P.6
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79
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T. Watanabe, H. Yokoyama, Y. Tanaka, J. Inoue and M. Ogata: J. Phys. Soc. Jpn. 73 (2004) 3404.
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(2004)
J. Phys. Soc. Jpn
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Watanabe, T.1
Yokoyama, H.2
Tanaka, Y.3
Inoue, J.4
Ogata, M.5
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K. Kuroki, T. Kimura, R. Arita, Y. Tanaka and Y. Matsuda: Phys. Rev. B 65 (2002) 100516.
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Phys. Rev. B
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Kuroki, K.1
Kimura, T.2
Arita, R.3
Tanaka, Y.4
Matsuda, Y.5
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33847387050
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The effect of difference (i, namely of t″/t, must be slight, because, according to Fig. 2 in ref. 23, the optimized |t″/t| is small both for the conductive (U/t ≲ 8.5) and insulating (U/t ≲ 8.5) phases. The effect of difference (ii, namely of putting μ′, μ in ΨLiu, manifests itself to some extent, because, as in Figs. 4(d) and 4e, the optimized values of μ and μ′ are quite different, especially in the insulating phase. Thus, it is possible that ΨLiu becomes quantitatively worse than ΨdQ for U ≲ Uc; better results would be obtained, if μ′, 0 is used instead of μ′, μ in ΨLiu
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Liu.
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90
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33847394451
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In ref. 23, the system-size dependence of the gap parameter Δ0/t* for U/t, 9.5 (in the insulating regime) is shown in the inset of Fig. 1. Because the finite Δ0/ t* does not necessarily indicate the realization of SC, as we have mentioned, it is useless to check whether Δ0/t* remains finite for L → ∞, in order to determine whether or not SC arises
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0/t* remains finite for L → ∞, in order to determine whether or not SC arises.
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