RT Journal Article
T1 Exactly solvable D-N-type quantum spin models with long-range interaction
A1 Basu Mallick, B.
A1 Finkel Morgenstern, Federico
A1 González López, Artemio
AB We derive the spectra of the D-N-type Calogero (rational) su(m) spin model, including the degeneracy factors of all energy levels. By taking the strong coupling limit of this model, in which its spin and dynamical degrees of freedom decouple, we compute the exact partition function of the su(m) Polychronakos-Frahm spin chain of D-N type. In particular, we show that this partition function cannot be obtained as a limiting case of its BCN counterpart. With the help of the partition function we study several statistical properties of the chain's spectrum, such as the density of energy levels and the distribution of spacings between consecutive levels.
PB Elsevier
SN 0550-3213
YR 2009
FD 2009-05-11
LK https://hdl.handle.net/20.500.14352/44677
UL https://hdl.handle.net/20.500.14352/44677
LA eng
NO [1] F. Calogero, J. Math. Phys. 12 (1971) 419. [2] B. Sutherland, Phys. Rev. A 4 (1971) 2019. [3] B. Sutherland, Phys. Rev. A 5 (1972) 1372. [4] M.A. Olshanetsky, A.M. Perelomov, Phys. Rep. 94 (1983) 313. [5] F.D.M. Haldane, Phys. Rev. Lett. 60 (1988) 635. [6] B.S. Shastry, Phys. Rev. Lett. 60 (1988) 639. [7] A.P. Polychronakos, Phys. Rev. Lett. 70 (1993) 2329. [8] Z.N.C. Ha, Quantum Many-body Systems in One Dimension, Advances in Statistical Mechanics, vol. 12, World Scientific, Singapore, 1996. [9] M.V.N. Murthy, R. Shankar, Phys. Rev. Lett. 73 (1994) 3331. [10] A.P. Polychronakos, J. Phys. A: Math. Gen. 39 (2006) 12793. [11] H. Azuma, S. Iso, Phys. Lett. B 331 (1994) 107. [12] C.W.J. Beenakker, B. Rajaei, Phys. Rev. B 49 (1994) 7499. [13] M. Caselle, Phys. Rev. Lett. 74 (1995) 2776. [14] N. Taniguchi, B.S. Shastry, B.L. Altshuler, Phys. Rev. Lett. 75 (1995) 3724. [15] P.J. Forrester, Nucl. Phys. B 416 (1994) 377. [16] H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 66 (1997) 345. [17] T.H. Baker, P.J. Forrester, Nucl. Phys. B 492 (1997) 682. [18] D. Bernard, M. Gaudin, F.D.M. Haldane, V. Pasquier, J. Phys. A: Math. Gen. 26 (1993) 5219. [19] K. Hikami, Nucl. Phys. B 441 (1995) 530. [20] B. Basu-Mallick, A. Kundu, Nucl. Phys. B 509 (1998) 705. [21] Z.N.C. Ha, F.D.M. Haldane, Phys. Rev. B 46 (1992) 9359. [22] K. Hikami, M. Wadati, J. Phys. Soc. Jpn. 62 (1993) 469. [23] J.A. Minahan, A.P. Polychronakos, Phys. Lett. B 302 (1993) 265. [24] B. Sutherland, B.S. Shastry, Phys. Rev. Lett. 71 (1993) 5. [25] H. Frahm, J. Phys. A: Math. Gen. 26 (1993) L473. [26] D. Bernard, V. Pasquier, D. Serban, Europhys. Lett. 30 (1995) 301. [27] T. Yamamoto, O. Tsuchiya, J. Phys. A: Math. Gen. 29 (1996) 3977. [28] A.P. Polychronakos, Nucl. Phys. B 419 (1994) 553. [29] F. Finkel, A. González-López, Phys. Rev. B 72 (2005) 174411. [30] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Phys. Rev. B 77 (2008) 214422. [31] A. Enciso, F. Finkel, A. González-López, M.A. Rodríguez, Nucl. Phys. B 707 (2005) 553. [32] B. Basu-Mallick, H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 68 (1999) 3219. [33] B. Basu-Mallick, N. Bondyopadhaya, Nucl. Phys. B 757 (2006) 280. [34] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Nucl. Phys. B 806 (2009) 684. [35] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Europhys. Lett. 83 (2008) 27005. [36] M.V. Berry, M. Tabor, Proc. R. Soc. London A 356 (1977) 375. [37] T. Yamamoto, Phys. Lett. A 208 (1995) 293. [38] E. Corrigan, R. Sasaki, J. Phys. A: Math. Gen. 35 (2002) 7017. [39] S. Ahmed, Lett. Nuovo Cimento 22 (1978) 371. [40] C.F. Dunkl, Commun. Math. Phys. 197 (1998) 451. [41] F. Finkel, D. Gómez-Ullate, A. González-López, M.A. Rodríguez, R. Zhdanov, Nucl. Phys. B 613 (2001) 472. [42] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, vol. 9, Springer-Verlag, New York, 1972. [43] J. Cigler, Monatsh. Math. 88 (1979) 87. [44] T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep. 299 (1998) 189. [45] B. Basu-Mallick, N. Bondyopadhaya, K. Hikami, D. Sen, Nucl. Phys. B 782 (2007) 276.
NO ©2008 Elsevier B.V. All rights reserved.This work was partially supported by Spain’s DGI under grant No. FIS2005-00752  and by the Complutense University and Madrid’s DGUI under grant No. GR74/07- 910556.
NO DGI, Spain
NO Complutense University
NO DGUI, Madrid
DS Docta Complutense
RD 18 may 2024