In this paper, we investigate Yangian symmetry for the three-spin-1/2 and four-spin-1/2 Heisenberg XXX models. Applying Yangian Y(sl(2)) theory to three-spin-1/2 and four-spin-1/2 systems, we construct Yangian Y(sl(2)) realizations for these systems. We show that these Yangian realizations can be used to describe three-spin-1/2 and four-spin-1/2 Heisenberg XXX models. The Yangian operators as shift operators are also studied in this paper.

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References

V. G. Drinfel'd, Sov. Math. Dokl. 31, 254 (1985). Web of Science, Google Scholar
M. Jimbo, Lett. Math. Phys. 10, 63 (1985), DOI: 10.1007/BF00704588. Web of Science, Google Scholar
M. Jimbo, Lett. Math. Phys. 11, 247 (1986), DOI: 10.1007/BF00400222. Web of Science, Google Scholar
D. Bernard, Commun. Math. Phys. 142 (1991) 99; D. Bernard and G. Felder, Nucl. Phys. B 365 (1991) 98 . Google Scholar
F. D. M. Haldane, Phys. Rev. Lett. 69, 2021 (1992), DOI: 10.1103/PhysRevLett.69.2021. Web of Science, Google Scholar
F. D. M. Haldane, Solvable Quantum Many-Body Problems Tianjin Sixth Nankai: International Workshop (Nankai University, Tianjin, 1993) . Google Scholar
D. Bernard, Int. J. Mod. Phys. B 7, 3517 (1993), DOI: 10.1142/S0217979293003371. Link, Web of Science, Google Scholar
K. Hikami, Nucl. Phys. B 441, 530 (1995), DOI: 10.1016/0550-3213(95)00035-Q. Web of Science, Google Scholar
X. B. Peng, C. M. Bai and M. L. Ge, Ann. Phys. 326, 216 (2011), DOI: 10.1016/j.aop.2010.10.005. Web of Science, Google Scholar
C. F. Sunet al., Ann. Phys. 333, 34 (2013), DOI: 10.1016/j.aop.2013.02.007. Web of Science, Google Scholar
D. B. Uglov, Phys. Lett. A 190, 238 (1994), DOI: 10.1016/0375-9601(94)90748-X. Web of Science, Google Scholar
F. Göhmann and V. Inozemtsev, Phys. Lett. A 214, 161 (1996). Web of Science, Google Scholar
F. H. L. Essler et al. , The One-Dimensional Hubbard Model ( Cambridge University Press , Cambridge , 2005 ) . Google Scholar
F. D. M. Haldaneet al., Phys. Rev. Lett. 69, 2021 (1992), DOI: 10.1103/PhysRevLett.69.2021. Web of Science, Google Scholar
F. D. M. Haldane, Phys. Rev. Lett. 60, 635 (1988), DOI: 10.1103/PhysRevLett.60.635. Web of Science, Google Scholar
V. I. Inozemtsev, J. Stat. Phys. 59, 1143 (1990), DOI: 10.1007/BF01334745. Web of Science, Google Scholar
B. S. Shastry, Phys. Rev. Lett. 60, 639 (1988), DOI: 10.1103/PhysRevLett.60.639. Web of Science, Google Scholar
D. Schuricht, J. Phys. A, Math. Theor. 41, 015208 (2008), DOI: 10.1088/1751-8113/41/1/015208. Web of Science, Google Scholar
J. B. Parkinson and D. J. J. Farnell, Lect. Notes Phys. 816, 7 (2010), DOI: 10.1007/978-3-642-13290-2_2. Google Scholar
J. M. Kosterlitz and D. J. Thouless, J. Phys. C, Solid State Phys. 6, 1181 (1973), DOI: 10.1088/0022-3719/6/7/010. Web of Science, Google Scholar
M. L. Geet al., Czech. J. Phys. 50, 1229 (2000), DOI: 10.1023/A:1022852722391. Web of Science, Google Scholar