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Volumn 40, Issue 7, 1989, Pages 4621-4626

Spectrum of the biquadratic spin-1 antiferromagnetic chain

Author keywords

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Indexed keywords


EID: 0000959809     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.40.4621     Document Type: Article
Times cited : (172)

References (55)
  • 2
    • 0000484067 scopus 로고
    • Competing bilinear and biquadratic exchange couplings in spin-1 Heisenberg chains
    • (1987) Physical Review B , vol.36 , pp. 8642
    • Sólyom, J.1
  • 22
    • 84931500497 scopus 로고    scopus 로고
    • in their study of a 19-vertex model that arises from two-dimensional O ( n ) models.
  • 23
    • 0041766464 scopus 로고
    • Equivalences between q-state vertex models and q2-state Potts models have been discussed, in a different context, by
    • (1986) J. Stat. Phys. , vol.42 , pp. 727
    • Perk, J.H.H.1    Wu, F.Y.2
  • 24
    • 84931500478 scopus 로고    scopus 로고
    • in these cases the resulting Potts models generally have multispin interactions.
  • 29
    • 84931500477 scopus 로고    scopus 로고
    • For the q-state Potts model, the factor 3 in (8) is replaced by sqrt q.
  • 36
    • 84931500480 scopus 로고    scopus 로고
    • We have checked this by direct diagonalization of the two Hamiltonians for L = 2 and L = 3.
  • 41
    • 84931500479 scopus 로고    scopus 로고
    • In the conventional (Euclidean) formulation of the Potts model 1 / Finf( λ ) corresponds to the bulk correlation length.
  • 42
    • 84931500482 scopus 로고    scopus 로고
    • Since for these states zj= ei kj with kj real, is convenient to solve (23) in their logarithmic form (see Ref. 23). However, care must be taken to define the correct branches of the inverse tangent function.
  • 49
    • 84931500481 scopus 로고    scopus 로고
    • Technically, these calculations assumed periodic boundary conditions rather than free ends. The analysis of Ref. 23 can be extended to confirm directly that in the limit M -> inf the choice of boundary conditions does not affect the value of the ground-state energy per site.
  • 53
    • 84931500484 scopus 로고    scopus 로고
    • have shown that EXXZ0( M , θ = 0 ) = M einf + O ( e-cM ) , ~ c > 0. However, the more complex distribution of the zeros of the Bethe ansatz equations for θ != 0 makes an extension of their method to this case difficult. Specifically, the effect of a nonzero value of theta is to perturb the zeros off the unit circle.
  • 54
    • 84931500483 scopus 로고    scopus 로고
    • Sólyom's parameter delta is related to lambda by λ = ( 1 + δ ) / ( 1 - δ ).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.