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3 Lieb-WuHubbard Minoru Takahashi, Prog. Theor. Phys. 42, (1969)

4 Minoru Takahashi, Prog. Theor. Phys. 43, 1619 (1970)

5 Bethe ansatz XXX Hulthen XXZ Orbach, Walker XYZ Baxter 1972 Boson Lieb-Liniger 1963 Fermion(s=1/2) Gaudin, Yang 1967 Fermion(s>1/2, c>0) Sutherland 1968 Fermion(s>1/2, c<0) Takahashi, Yang D Hubbard model Lieb-Wu 1968 Fredholm type linear integral equation

6 Minoru Takahashi, Prog. Theor. Phys. 46, (1971)

7 Minoru Takahashi, Prog. Theor. Phys. 46, (1971)

8 Minoru Takahashi, Prog. Theor. Phys. 47, (1972)

9 Minoru Takahashi and Masuo Suzuki, Prog. Theor. Phys. 48, (1972)

10 Yang-Yang Boson Gaudin -Takahashi equation, 0, string Hubbard (k- string) cos /nn-1 cos * rational number XXZ XYZ Takahashi-Suzuki equation Yang-Yang gtype non-linear integral equation

11 Low-temperature thermodynamics of 1D Hubbard Minoru Takahashi, Prog. Theor. Phys. 52, (1974)

12 Low-temperature thermodynamics of XXZ and XYZ chain Minoru Takahashi, Prog. Theor. Phys. 50, (1973)

13 Minoru Takahashi, Prog. Theor. Phys. 50, (1973)

14 Ferromagnet at Low-Temperature Takahashi-Yamada, Schlottmann 1985 Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, (1985)

15 Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, (1985)

16 Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, (1985)

17 Modified spin-wave theory for ferromagnet In 1D case MSW gives Reprinted with permission from Minoru Takahashi, Phys. Rev. Lett. 58, (1987) Copyright (1987) by the American Physical Society.

18 Self consistent equation Reprinted with permission from Minoru Takahashi, Phys. Rev. Lett. 58, (1987), Copyright (1987) by the American Physical Society.

19 Shltt Schlottmann s low-temerature t susceptibility Reprinted with permission from Minoru Takahashi, Phys. Rev. Lett. 58, (1987), Copyright (1987) by the American Physical Society.

20 2D square lattice system and classical system Reprinted with permission from Minoru Takahashi, Phys. Rev. B 36, (1987), Copyright (1987) by the American Physical Society.

21 Modified spin-wave theory for square lattice antiferromagnet Phys. Rev. B (1989),Arovas-Auerbach, Hirsch-Tang, Reprinted with permission from Minoru Takahashi, Phys. Rev. B 40, (1989), Copyright (1989) by the American Physical Society.

23 Quantum Monte Carlo 1.Formulation of path integral Monte Carlo method 2.Application to He4 and 2D electron gas 3.Elementary excitation and correlation function of Haldane chain

24 Minoru Takahashi and Masatoshi Imada, J. Phys. Soc. Jpn. 53, (1984) Masatoshi Imada and Minoru Takahashi, J. Phys. Soc. Jpn. 53, (1984)

25 Minoru Takahashi and Masatoshi Imada, J. Phys. Soc. Jpn. 53, (1984)

26 Reprinted with permission from Minoru Takahashi, Phys. Rev. Lett. 62, (1989), Copyright (1989) by the American Physical Society. Seishi Takagi, Hiroyuki Deguchi, Kazuyoshi Takeda, Masaki Mito and Minoru, J. Phys. Soc. Jpn. 65, (1996)

27 Logarithmic anomaly of anti- ferromagnetic chain p.123

28 Reprinted with permission from Sebastian Eggert, Ian Affleck, and Minoru Takahashi, Phys. Rev. Lett. 73, (1994) Copyright (1994) by the American Physical Society. Reprinted with permission from Jill C. Bonner and Michael E. Fisher, Phys. Rev. 135, A640-A658 (1964) Copyright (1964) by the American Physical Society.

29 Seishi Takagi, Hiroyuki Deguchi, Kazuyoshi Takeda, Masaki Mito, and Minoru Takahashi, J. Phys. Soc. Jpn. 65, (1996) Reprinted with permission from N. Motoyama, H. Eisaki, and S. Uchida, Phys. Rev. Lett. 76, (1996) Copyright (1996) by the American Physical Society.

30 Four-spin interaction term M. Takahashi, J. Phys. C: Solid State Phys. 10, (1977)

31 M. Takahashi, J. Phys. C: Solid State Phys. 10, (1977)

32 M. Takahashi, J. Phys. C: Solid State Phys. 10, (1977)

33 Reprinted with permission from Reprinted with permission from Y. Nakazawa, M. Tamura, N. Shirakawa, D. Shiomi, M. Takahashi, M. Kinoshita, and M. Ishikawa, Phys. Rev. B 46, (1992) Copyright (1992) by the American Physical Society.

34 Reprinted with permission from Reprinted with permission from Y. Nakazawa, M. Tamura, N. Shirakawa, D. Shiomi, M. Takahashi, M. Kinoshita, and M. Ishikawa, Phys. Rev. B 46, (1992) Copyright (1992) by the American Physical Society.

36 Haldane chain Reprinted with permission from Minoru Takahashi, Phys. Rev. B 50, (1994) Copyright (1994) by the American Physical Society. Reprinted with permission from Shaolong Ma, Collin Broholm, Daniel H. Reich, B. J. Sternlieb, and R. W. Erwin, Phys. Rev. Lett. 69, (1992) Copyright (1992) by the American Physical Society.

37 Reprinted with permission from Minoru Takahashi, Phys. Rev. B 50, (1994) Copyright (1994) by the American Physical Society. Reprinted with permission from Shaolong Ma, Collin Broholm, Daniel H. Reich, B. J. Sternlieb, and R. W. Erwin, Phys. Rev. Lett. 69, (1992) Copyright (2002) by the American Physical Society.

38 After New simplified form of TBA equations This equation is convenient to get the high temperature expansion of thermodynamic quantities.xxz chain and Perk-Schultz model. 2. High-temperature expansion of Hubbard model and TBA equations 3. Calculation of correlation functions of XXX and XXZ chain

39 New simplified form of TBA equations

41 Reprinted with permission from Masahiro Shiroishi and Minoru Takahashi, Phys. Rev. Lett. 89, (2002) Copyright (2002) by the American Physical Society.

42 High temperature expansion of Hubbard model Reprinted with permission from Minoru Takahashi and Masahiro Shiroishi, Phys. Rev. B 65, (2002) Copyright (2002) by the American Physical Society.

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