Abstract
Thermo field dynamics of quantum spin systems is formulated, which gives a new variational principle at finite temperatures. The KMS relation is reformulated as identities among thermal vacuum states. Path integral formulations of the thermal vacuum state are given, which yield a new “thermo field Monte Carlo method.” Thermo field dynamics of finite-spin systems are studied in detail as simple examples of the present method. Pertubational expansion methods of the thermal state and time-dependent state are also given.
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References
L. Leplae, F. Mancini, and H. Umezawa,Phys. Rep. 10C:151 (1974).
Y. Takahashi and H. Umezawa,Collect. Phenom. 2:55 (1975).
H. Umezawa, H. Matsumoto, and M. Tachiki,Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, New York, 1982).
M. Suzuki, inProgress in Quantum Field Theory, H. Ezawa and S. Kamefuchi, eds. (North-Holland, Amsterdam, 1986).
H. Matsumoto, in the same book as in Ref. 4.Progress in Quantum Field Theory, H. Ezawa and S. Kamefuchi, eds. (North Holland, Amsterdam, 1985).
H. Matsumoto, Y. Nakano, and H. Umezawa,Phys. Lett. 100A:125 (1984).
T. Arimitsu and H. Umezawa,Prog. Theor. Phys. 74:429 (1985).
R. Kubo,J. Phys. Soc. Ppn. 17:1100 (1962).
R. Kubo,J. Phys. Soc. Jpn. 12:570 (1957).
P. Martin and J. Schwinger,Phys. Rev. 115:1342 (1959).
M. Suzuki,Commun. Math. Phys. 51:183 (1976);Commun. Math. Phys. 57:193 (1977).
M. Suzuki,Prog. Theor. Phys. 56:1454 (1976).
M. Suzuki,J. Math. Phys. 26:601 (1985).
M. Suzuki,Phys. Rev. B 31:2957 (1985).
H. Betsuyaku,Phys. Rev. Lett. 53:629 (1984);Prog. Theor. Phys. 73:319 (1985).
J. Kuti,Phys. Rev. Lett. 49:183 (1982).
R. Blankenbecler and R. L. Sugar,Phys. Rev. D 27:1304 (1983).
M. Suzuki, S. Miyashita, and A. Kuroda,Prog. Theor. Phys. 58:1377 (1977).
M. Suzuki,Phys. Lett. IIIA:441 (1985); see also M. Suzuki,J. Phys. Soc. Jpn. 54:4483 (1985).
J. E. Hirsch, D. J. Scalapino, R. L. Sugar, and R. Blakenbecler,Phys. Rev. Lett. 47:1628 (1981);Phys. Rev. B 26:5033 (1982).
P. W. Anderson,Mat. Res. Bull. 8:153 (1973); P. Fazekas, and P. W. Anderson,Philos. Mag. 30:423 (1974).
K. Hirakawa, H. Ikeda, H. Kadowaki, and K. Ubukoshi,J. Phys. Soc. Jpn. 52:2822 (1983); K. Hirakawa, H. Kadowaki, and K. Ubukoshi,J. Phys. Soc. Jpn. 54:3526 (1985).
M. Suzuki,J. Phys. Soc. Jpn. 21:2274 (1966).
P. W. Anderson,Phys. Rev. 86:694 (1952).
M. Suzuki and S. Miyashita,Can. J. Phys. 56:902 (1978); S. Miyashita,J. Phys. Soc. Jpn. 53:44 (1984).
T. Oguchi, H. Nishimori, and Y. Taguchi,J. Phys. Soc. Jpn. 55:323 (1986).
S. Fujiki and D. D. Betts, preprints.
F. A. Brezin,The Method of Second Quantization (Academic Press, New York, 1966).
M. Suzuki,Prog. Theor. Phys. 56:1007 (1976).
M. H. Kalos,Monte Carlo Methods in Quantum Problems (D. Reidel, Dordrecht, 1984).
K. Binder,Monte Carlo Methods in Statistical Physics I (Springer-Verlag, Heidelberg, 1979).
O. G. Mouritsen,Computer Studies of Phase Transitions and Critical Phenomena (Springer-Verlag, Heidelberg, 1984).
M. Barma and B. S. Shastry,Phys. Lett. 61A:15 (1977).
H. De Raedt and A. Langendijk,Phys. Rev. Lett. 46:77 (1981);J. Stat. Phys. 27:731 (1982);Phys. Rev. Lett. 49:1552 (1982);Phys. Rev. 24B:463 (1981); H. De Raedt, B. De Raedt, and A. Lagendijk,Z. Phys. B57:209 (1974); H. De Raedt and B. De Raedt,Phys. Rev. 28A:3575 (1983), and H. De Raedt and A. Lagendijk,Phys. Rep. 127:233 (1985).
J. J. Cullen and D. P. Landau,Phys. Rev. B27:297 (1983).
A. Wiesler,Phys. Lett. A89:359 (1982).
J. W. Lyklema,Phys. Rev. Lett. 49:88 (1982);Phys. Rev. B 27:3108 (1983).
M. Kolb,Phys. Rev. Lett. 51:1696 (1983).
H. De Raedt, J. Fivez, and A. Lagendijk,Solid State Sciences Series, S. W. Lovesey, ed. (Springer, Berlin, 1984).
S. Chakravarty and D. V. Stein,Phys. Rev. Lett. 23:583 (1982).
Y. Avishai and J. Richert,Phys. Rev. Lett. 50:1175 (1983);Phys. Rev. Lett. 51:1103 (1983).
M. Takahashi and M. Imada,J. Phys. Soc. Jpn. 53:963 (1984).
T. Sakaguchi, K. Kubo, and S. Takada,J. Phys. Soc. Jpn. 54:861 (1985).
S. Homma, H. Matsuda, and N. Ogita,Prog. Theor. Phys. 72:1245 (1984).
H. Takano,Prog. Theor. Phys. 73:332 (1985).
T. Tsuzuki,Prog. Theor. Phys. 73:1352 (1985).
M. Takasu, S. Miyashita, and M. Suzuki,Prog. Theor. Phys. (submitted).
M. Suzuki,J. Stat. Phys. (1986, to appear).
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Suzuki, M. Thermo field dynamics of quantum spin systems. J Stat Phys 42, 1047–1070 (1986). https://doi.org/10.1007/BF01010461
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DOI: https://doi.org/10.1007/BF01010461