Quantum Integrability in Systems with Finite Number of Levels

Journal of Statistical Physics

Volumn 150, Issue 4, 2013, Pages 704-721

  Yuzbashyan, Emil A ^a   Shastry, B Sriram ^b  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dynamical conservation laws; Energy level statistic; Integrability; Yang Baxter

Indexed keywords

EID: 84874276098     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-013-0689-9     Document Type: Article

References (41)

1. Yuzbashyan, E. A., Altshuler, B. L., Shastry, B. S.: J. Phys. A, Math. Gen. 35, 7525 (2002).
2. Shastry, B. S.: J. Phys. A, Math. Gen. 38, L431 (2005).
3. Owusu, H. K., Wagh, K., Yuzbashyan, E. A.: J. Phys. A, Math. Theor. 42, 035206 (2009).
4. Shastry, B. S.: J. Phys. A, Math. Theor. 44, 052001 (2011).
5. Owusu, H. K., Yuzbashyan, E. A.: J. Phys. A, Math. Theor. 44, 395302 (2011).
6. Baxter, R. J.: Physica A 106, 18 (1981).
7. Drinfel'd, V. G.: Sov. Math. Dokl. 32, 254 (1985).
8. Davies, B., Foda, O., Jimbo, M., Miwa, T., Nakayashiki, A.: Commun. Math. Phys. 151, 89 (1993).
9. Sutherland, B.: Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems. World Scientific, Singapore (2004).
10. Arnold, V. I.: Mathematical Methods of Classical Mechanics. Springer, New York (1978).
11. Perlis, S.: Theory of Matrices. Dover, New York (1991). Theorem 9-32.
12. von Neumann, J.: Ann. Math. 32, 191 (1931).
13. von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1996).
14. Weigert, S.: Physica D 56, 107 (1992).
15. Lieb, H., Wu, F. Y.: Phys. Rev. Lett. 20, 1445 (1968).
16. Lieb, H., Wu, F. Y.: Physica A 321, 1 (2003).
17. Heilmann, O. J., Lieb, E. H.: Ann. N. Y. Acad. Sci. 172, 583 (1971).
18. Nishino, A., Deguchi, T.: Phys. Rev. B 68, 075114 (2003).
19. Shastry, B. S.: Phys. Rev. Lett. 56, 1529 (1986). Ibid., 56, 2453 (1986).
20. Shastry, B. S.: J. Stat. Phys. 50, 57 (1988).
21. Poilblanc, D., et al.: Europhys. Lett. 22, 537 (1993).
22. Caux, J.-S., Mossel, J.: J. Stat. Mech. 2011, P02023 (2011).
23. Relano, A., Dukelsky, J., Gomez, J. M. G., Retamosa, J.: Phys. Rev. E 70(2), 026208 (2004).
24. Sklyanin, E.: J. Sov. Math. 47, 2473 (1989).
25. Sklyanin, E.: Prog. Theor. Phys. Suppl. 118, 35 (1995).
26. Cambiaggio, M. C., Rivas, A. M. F., Saraceno, M.: Nucl. Phys. A 624, 157 (1997).
27. Lüscher, M.: Nucl. Phys. B 117, 475 (1976).
28. Grosse, H.: Lett. Math. Phys. 18, 151 (1989).
29. Grabowski, M. P., Mathieu, P.: Ann. Phys. 243, 299 (1995).
30. Links, J., Zhou, H.-Q., McKenzie, R. H., Gould, M. D.: Phys. Rev. Lett. 86, 5096 (2001).
31. Zhou, H., Jiang, L., Tang, J.: J. Phys. A, Math. Gen. 23, 213 (1990).
32. Fuchssteiner, B.: In: Symmetries and Nonlinear Phenomena, pp. 22-50. World Scientific, Singapore (1988).
33. Hansen, D., Yuzbashyan, E. A., Shastry, B. S.: in preparation.
34. Yang, C. N.: Phys. Rev. 168, 1920 (1968).
35. Shastry, B. S., Sutherland, B.: Phys. Rev. Lett. 65, 243 (1990).
36. Baxter, R. J.: Phys. Rev. Lett. 26, 832 (1971).
37. Berry, M. V., Tabor, M.: Proc. R. Soc. Lond. Ser. A 356, 375 (1977).
38. Owusu, H. K., Yuzbashyan, E. A., Shastry, B. S.: unpublished.
39. Sutherland, B.: Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory. Lecture Notes in Physics, vol. 242, p. 66. Springer, Berlin (1985).
40. McGuire, J. B.: J. Math. Phys. 6, 432 (1965).
41. Owusu, H. K., Shastry, B. S.: (2012, to be published).