Algebraic Bethe ansatz for a discrete-state BCS pairing model

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 13, 2002, Pages 1345021-13450213

  Von Delft, Jan ^a,b   Poghossian, R ^a  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MATHEMATICS; PHYSICS;

EID: 0242354804     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.134502     Document Type: Article

References (29)

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22. After the bulk of this work had been completed, three papers appeared in which some such correlation functions indeed were calculated: L. Amico and A. Osterloh, Phys. Rev. Lett. 88, 127003 (2002); H.-Q. Zhou, J. Links, R.H. McKenzie, and M.D. Gould, Phys. Rev. B 65, 060502 (2002) and, by the same authors, very recently also cond-mat/0110105 (unpublished).
23. After the bulk of this work had been completed, three papers appeared in which some such correlation functions indeed were calculated: L. Amico and A. Osterloh, Phys. Rev. Lett. 88, 127003 (2002); H.-Q. Zhou, J. Links, R.H. McKenzie, and M.D. Gould, Phys. Rev. B 65, 060502 (2002) and, by the same authors, very recently also cond-mat/0110105 (unpublished).
24. k Wess-Zumino-Witten conformal field theory, in the singular limit when the level k goes to - 2, see G. Sierra, Nucl. Phys. B 572, 517 (2000).
25. i given in Ref. 5 is related to our Eq. (10) by the transformation (6).
26. l diverge proportional to g for large g [R. Richardson (private communication)].
27. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, New York, 1982).
28. In fact, it is possible to satisfy Eq. (47), and hence maintain integrability, using more general choices of K: for the XXX model, Eq. (47) holds for an arbitrary 2 x 2 K-matrix. For the XXZ model, Eq. (47) holds for any diagonal K-matrix, or any purely-off-diagonal K-matrix (i.e., vanishing diagonal elements). For both the XXX and XXZ models, though, only the case of a diagonal K-matrix is solvable by conventional Betheansatz methods. The off-diagonal cases are solvable, however, using Sklyanin's method of separation of variables.
29. Note that our derivation below of the mutually commuting operators in the quasiclassical limit does not need to introduce the notion of a "quantum determinant," and thus is slightly more direct than the method used by Sklyanin in Ref. 12.