Abstract
Low-dimensional quantum spin systems are interacting many body systems for which several rigorous results are known. Powerful techniques like the Bethe Ansatz provide exact knowledge of the ground state energy and low-lying excitation spectrum. A large number of compounds exist which can effectively be described as low-dimensional spin systems. Thus many of the rigorous results are also of experimental relevance. In these lectures, an introduction is given to quantum spin systems and the rigorous results known for such systems. Some general theorems and exactly-solvable models are discussed. An elementary introduction to the Bethe Ansatz technique is given.
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Bibliography
C.K. Majumdar and D.K. Ghosh, J.Math. Phys. 10, 1388 (1969); see also Ref. [6].
F.D.M. Haldane, Phys. Rev. Lett. 60, 635 (1988);
B. S. Shastry, Phys. Rev. Lett. 60, 639 (1988).
E. Westerberg, A. Furusaki, M. Sigrist and P.A. Lee, Phys. Rev. Lett. 75, 4302. (1995).
S.M. Bhattacharjee and S. Mukherji, J.Phys. A: Math. Gen. 31, L695 (1998).
E. Manousakis, Rev. Mod. Phys. 63, 1 (1991).
Interacting Electrons and Quantum Magnetism by A. Auerbach (Springer-Verlag, New York 1994).
E. Lieb and D.C. Mattis, J. Math. Phys. 3, 749 (1962).
W. Marshall, Proc. R. Soc. London Ser. A 232, 48 (1955).
E. Lieb, T.D. Schultz and D.C Mattis, Ann. Phys. 16, 407 (1961).
I. Affleck, J. Phys.: Condens. Matter 1, 3047 (1989).
M. Oshikawa, M. Yamanaka and I. Affleck, Phys. Rev. Lett. 78, 1984 (1997).
K. Hida, J.Phys. Soc. Jpn. 63, 2359 (1994).
M. D. Mermin and H. Wagner, Phys. Rev. Lett. 22, 1133 (1966).
F. Dyson, E.H. Lieb and B. Simon, J. Stat. Phys. 18, 335 (1978);
T. Kennedy, E.H. Lieb and B.S. Shastry, J. Stat. Phys. 53, 1019 (1988).
E.J. Neves and J.F. Perez, Phys. Lett. 114 A, 331 (1986).
I. Affleck, T. Kennedy, E.H. Lieb and H. Tasaki, Commun. Math. Phys. 115, 447 (1988).
Th. Jolicoeur and J.C. Le Guillou, Phys. Rev. B 40, 2727 (1989).
C. Zeng and V. Elser, Phys. Rev. B 51, 8318 (1995).
B. Canals and C. Lacroix, Phys. Rev. Lett. 80, 2933 (1998).
U. Bhaumik and I. Bose, Phys. Rev. B 58, 73 (1998).
B. Bernu, P. Lecheminant, C. Lhuillier and L. Pierre, Phys. Rev. B 50, 10048 (1994).
K. Ueda, H. Kontani, M. Sigrist and P.A. Lee, Phys. Rev. Lett. 76, 1932 (1996).
I. Bose and A. Ghosh, Phys. Rev. B 56, 3149 (1997).
E. Dagotto, Int. J. Mod. Phys. B 5, 907 (1991);
I. Bose, Physica A 186, 298 (1992).
B.S. Shastry and B. Sutherland, Phys. Rev. Lett. 47, 964 (1981).
S. Rao and D. Sen, Nucl. Phys. B 424, 547 (1994);
S. Rao and D. Sen, J.Phys. : Condens. Matter 9, 1837 (1997);
K. Nomura and K. Okamoto, J. Phys. A: Math. Gen. 27, 5773 (1994).
B.S. Shastry and B. Sutherland, Physica B 108, 1069 (1981).
I. Bose and P. Mitra, Phys. Rev. B 44, 443 (1991);
see also U. Bhaumik and I. Bose, Phys. Rev. B 52, 12489 (1995).
S. Miyahara and K. Ueda, Phys. Rev. Lett. 82, 3701 (1999).
F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983);
F.D.M. Haldane, Phys. Lett. A 93, 464 (1983).
J.P. Renard et al, Europhys. Lett. 3, 945 (1987);
M. Date and K. Kindo, Phys. Rev. Lett. 65, 1659 (1990).
I. Affleck, T. Kennedy, E.H. Lieb and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987).
M. Hagiwara et al, Phys. Rev. Lett. 65, 3181 (1990).
D.P. Arovas, A. Auerbach and F. D. M. Haldane, Phys. Rev. Lett. 60, 531 (1988).
G. Fáth and J. Sólyom, J. Phys.: Condens. Matter 5, 8983 (1993).
E. Dagotto and T.M. Rice, Science 271, 618 (1996).
T.M. Rice, Z.Phys.B 103, 165 (1997).
E. Dagotto, Rep. Prog. Phys. 62, 1525 (1999), cond-mat/9908250.
I. Bose and S. Gayen, Phys. Rev. B 48, 10653 (1993);
Y. Xian, Phys. Rev. B 52, 12485 (1995).
A. Ghosh and I. Bose, Phys. Rev. B 55, 3613 (1997).
I. Bose and S. Gayen, J.Phys.: Condens. Matter 11, 6427 (1999).
H. Bethe, Z. Physik 71, 205 (1931).
L. Hulthén, Arkiv. Mat. Astron. Fys. 26A, 11 (1938).
E. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963);
E. Lieb, Phys. Rev. 130, 1616 (1963);
M. Gaudin, Phys. Lett. 24A, 55 (1967);
C.N. Yang, Phys. Rev. Lett. 19, 1312 (1967);
C.N. Yang and C.P. Yang, J.Math.Phys. 10, 1115 (1969).
E. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968).
B. Sutherland, Phys. Rev. Lett. 34, 1083 (1975); ibid 35, 185 (1975).
B. Sutherland, Phys. Rev. B 12, 3795 (1975).
N. Andrei, Phys. Rev. Lett. 45, 379 (1980).
P.B. Wiegmann, J.Phys. C 14, 1463 (1981);
V.M. Filyov, A.M. Tsvelick and P.G. Wiegmann, Phys. Lett. 81 A, 175 (1981).
P.A. Bares and G. Blatter, Phys. Rev. Lett. 64, 2567 (1990).
I. Bose in Models and Techniques in Statistical Physics ed. by S.M. Bhattacharjee (Narosa, New Delhi India 1997), p.144.
A. Ovchinnikov, Zh. Eksperim. i Teor. Fiz. 56, 1354 (1969).
J.B. Torrance and M. Tinkham, Phys. Rev. 187, 587 (1969); ibid 187, 59 (1969).
D.F. Nicoli and M. Tinkham, Phys. Rev. B 9, 3126 (1974).
J. des Cloizeaux and J.J. Pearson, Phys. Rev. 128, 2131 (1962).
L.D. Faddeev and L.A. Takhtajan, Phys. Lett. 85A, 375 (1981); see also C.K. Majumdar in Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory ed. by B.S. Shastry, S.S. Jha and V. Singh (Springer-Ver lag, Berlin Heidelberg 1985).
D.A. Tennant, T.G. Perring, R.A. Cowley and S.E. Nagler, Phys. Rev. Lett. 70, 4003 (1993).
L.A. Takhtajan in Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory ed. by B.S. Shastry, S.S. Jha and V. Singh (Springer-Verlag, Berlin Heidelberg 1985).
I. Bose in Models and Techniques of Statistical Physics ed. by S.M. Bhattacharjee (Narosa, New Delhi India 1997), p. 156.
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Bose, I. (2001). Low-dimensional Quantum Spin Systems. In: Field Theories in Condensed Matter Physics. Texts and Readings in Physical Sciences. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-07-1_8
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