UTokyo OpenCourseWare...Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, 2808-2811 (1985)...

��

1. �� !"#$�%&2. '()*+,-.�/ 0!"#12%"##�&

3. ��3-�4567�898:�;<!"#1%"##�&

4 =�+,->?@

� ¡¢£ ¤¥¦¦§¨©§ª «¬¨©§¨®¯¬°±

²³ ¢ ´µ ¶·

££±£ ¸¹±

º »� ¼½¡¢¾ ·§ª¯©©¿À

£ ¸¹£º£¾ ½¹£¿£À ÁÂ£ Ã( ÄÅ

ÆÇÈÉÊ©¦ª ¶©ËÌÌÆ© É©Í®©¥ÎªÍÏÎ©

£ ÐÑ£££± ~Â[ÒÓ ~ÁÔÕÖ ÔÁ ÔÁ ×Áº ÔÕÖ ÔÁ[ÔÁ[×Á

¾ ØÙ Í¿ ÚÛ Ü¥¨ÝÀ ÂÞ[ßÑ à©°¨áÝ âªª¨£ ~Â

º±±± ãä åÛº æº æ¾ çÑ¿À ¯©©

"#21 Lieb-WuhlX"()HubbardKL�èéJ

êF0ëìílêF0î��ï

Minoru Takahashi, Prog. Theor. Phys. 42, 1098-1105 (1969) ‡

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

ðñòó`�IJKL�ôõö÷øù5ú�ZBethe ansatz J�ûüMN`ýtXuXXXKLþþþHulthen "#�1

KL O b h lk "#G1 "#G#XXZKLþþþOrbach, Walker "#G1�"#G#XYZKLþþþBaxter 1972�BosonþþþLieb-Liniger 1963�Boson Lieb-Liniger 1963�Fermion(s=1/2)þþþGaudin, Yang 1967�Fermion(s>1/2, c>0)þþþSutherland 1968( , )�Fermion(s>1/2, c

Minoru Takahashi and Masuo Suzuki, Prog. Theor. Phys. 48, 2187-2209 (1972) ‡

"#2# Yang-YanghlX"()�5�MNBoson��

þþþþ"��MN��ì�û��

"#$" Gaudin -Takahashi equation |�|�0 � string"#$" Gaudin Takahashi equation, |�|�0, � string

þþþþ��MN��ì�û��

"#$� "()�5�MN��["()HubbardKL�� (k-� string)

��cos �/n��n-1��MN��iû��

��cos �* rational number��C��MN��iu� cos � rational number��C��MN��iu

XXZ�XYZKL��

þþþTakahashi-Suzuki equation

Yang-Yang type non-linear integral equationg g yp g q

Low-temperature thermodynamics of 1D Hubbard


Low-temperature thermodynamics of XXZ and XYZ chainp y


Ferromagnet at Low-Temperature

Takahashi-Yamada Schlottmann 1985Takahashi-Yamada, Schlottmann 1985Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, 2808-2811 (1985) ‡

Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, 2808-2811 (1985) ‡

Modified spin-wave theory for ferromagnet

In 1D case MSW gives

Reprinted with permission fromMinoru Takahashi, Phys. Rev. Lett. 58, 168 - 170 (1987)Copyright (1987) by the American Physical Society. ‡

Self consistent equation

Reprinted with permission fromMinoru Takahashi, Phys. Rev. Lett. 58, , y ,168 - 170 (1987), Copyright (1987) by the American Physical Society. ‡

S hl tt ’ l t t tibilitSchlottmann’s low-temerature susceptibility

Reprinted with permission fromMinoru Takahashi, Phys. Rev. Lett. 58, , y ,168 - 170 (1987), Copyright (1987) by the American Physical Society. ‡

2D square lattice system and classical systemq y y

Reprinted with permission fromMinoru Takahashi, Phys. Rev. B 36, 3791 -, y ,3797 (1987), Copyright (1987) by the American Physical Society. ‡

Modified spin-wave theory for square lattice antiferromagnetModified spin wave theory for square lattice antiferromagnet

Phys. Rev. B40 2494 (1989),Arovas-Auerbach, Hirsch-Tang,

Reprinted with permission fromMinoru Takahashi, Phys. Rev. B 40, 2494 -, y ,2501 (1989), Copyright (1989) by the American Physical Society. ‡

Q t M t C lQuantum Monte Carlo

1.Formulation of path integral Monte Carlo methodmethod2.Application to He4 and 2D electron gas3.Elementary excitation and correlation function of Haldane chainfunction of Haldane chain

Masatoshi Imada and Minoru Takahashi, J. Phys. Soc. Jpn. 53, 3770-3781 (1984) ‡

Minoru Takahashi and Masatoshi Imada,J. Phys. Soc. Jpn. 53, 3871-3877 (1984) ‡

Minoru Takahashi and Masatoshi Imada J Phys Soc Jpn 53 3765 3769 (1984) ‡Minoru Takahashi and Masatoshi Imada, J. Phys. Soc. Jpn. 53, 3765-3769 (1984) ‡

Reprinted with permission fromMinoru Takahashi, Phys. Rev. Lett. 62, 2313 - 2316 (1989), Copyright (1989) by the American Physical Society. ‡

Seishi Takagi, Hiroyuki Deguchi, Kazuyoshi Takeda, Masaki Mito and Minoru,, ,J. Phys. Soc. Jpn. 65, 1934-1937 (1996) ‡

Logarithmic anomaly of antiLogarithmic anomaly of anti-ferromagnetic chainferromagnetic chain

��þ�� p.123 �� ‡

Reprinted with permission fromSebastian Eggert, Ian Affleck, and Minoru Takahashi, Phys Rev Lett 73 332 335 (1994)Phys. Rev. Lett. 73, 332 - 335 (1994)Copyright (1994) by the American Physical Society. ‡

Reprinted with permission fromJill C. Bonner and Michael E. Fisher, Phys. Rev. 135, A640-A658 (1964)Copyright (1964) by the American Physical Society. ‡

Reprinted with permission fromN Motoyama H Eisaki and S Uchida Phys RevN. Motoyama, H. Eisaki, and S. Uchida, Phys. Rev. Lett. 76, 3212 - 3215 (1996)Copyright (1996) by the American Physical Society. ‡

Seishi Takagi, Hiroyuki Deguchi, Kazuyoshi Takeda, Masaki Mito, and Minoru Takahashi,J. Phys. Soc. Jpn. 65, 1934-1937 (1996) ‡

Four-spin interaction termFour spin interaction term

M. Takahashi, J. Phys. C: Solid State Phys. 10, 1289-7301 (1977) ‡

M. Takahashi, J. Phys. C: Solid State Phys. 10, 1289-7301 (1977) ‡

CDEF9=��

Reprinted with permission fromReprinted with permission fromY. Nakazawa, M. Tamura, N. Shirakawa, D. Shiomi, M. Takahashi, M. Kinoshita, and M. Ishikawa, Phys. Rev. B 46, 8906-8914 (1992)Copyright (1992) by the American Physical Society. ‡

Reprinted with permission fromReprinted with permission fromY. Nakazawa, M. Tamura, N. Shirakawa, D. Shiomi, M. Takahashi, M. Kinoshita, and M. Ishikawa, Phys. Rev. B 46, 8906-8914 (1992)Copyright (1992) by the American Physical Society. ‡

Haldane chainHaldane chain

Reprinted with permission fromMinoru Takahashi, Phys. Rev. B 50, 3045 - 3051 (1994)Copyright (1994) by the American Physical Society. ‡

Reprinted with permission fromShaolong Ma, Collin Broholm, Daniel H. Reich, B. J. Sternlieb, and R. W. Erwin, Phys. Rev. Lett. 69, 3571 - 3574 (1992) Copyright (1992) by the American Physical Society. ‡

Reprinted with permission fromShaolong Ma, Collin Broholm, Daniel H. Reich, B. J. Sternlieb, and R. W. Erwin, Phys. Rev. Lett. 69, 3571-3574 (1992)Copyright (2002) by the American Physical Society. ‡

Reprinted with permission fromMinoru Takahashi, Phys. Rev. B 50, 3045 - 3051 (1994)Copyright (1994) by the American Physical Society. ‡

After 2000After 20001. New simplified form of TBA equations

This equation is convenient to get the high temperature expansion of thermodynamic p p yquantities.XXZ chain and Perk-Schultz model.2. High-temperature expansion of Hubbard model and TBA equationsmodel and TBA equations3. Calculation of correlation functions of XXX and XXZ chainXXX and XXZ chain

New simplified form of TBA equations

Reprinted with permission fromMasahiro Shiroishi and Minoru Takahashi, Phys. Rev. Lett. 89, 117201 (2002)Copyright (2002) by the American Physical Society. ‡

High temperature expansion of Hubbard model

Reprinted with permission fromMinoru Takahashi and Masahiro Shiroishi, Phys. Rev. B 65, 165104 (2002), y , ( )Copyright (2002) by the American Physical Society. ‡

UTokyo OpenCourseWare...Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, 2808-2811 (1985)...

Documents

Transcript of UTokyo OpenCourseWare...Minoru Takahashi and Miki Yamada, J. Phys. Soc. Jpn. 54, 2808-2811 (1985)...