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Volumn 9, Issue 2, 2000, Pages 133-159

Nonlinear σ model treatment of quantum antiferromagnets in a magnetic field

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; MAGNETIC FIELDS; MAGNETIZATION; NONLINEAR SYSTEMS; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; QUANTUM ELECTRONICS;

EID: 0033901571     PISSN: 00033804     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1521-3889(200002)9:2<133::AID-ANDP133>3.0.CO;2-Z     Document Type: Article
Times cited : (14)

References (49)
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    • (1983) Phys. Lett. , vol.93 A , pp. 464
    • Haldane, F.D.M.1
  • 2
    • 4244109353 scopus 로고
    • F. D. M. Haldane, Phys. Lett. 93A (1983) 464; Phys. Rev. Lett. 50 (1983) 1153
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 1153
  • 12
    • 0442316649 scopus 로고
    • H. J. Mikeska, J. Phys. C 13 (1980) 2913; A. F. Andreev, and V. I. Marchenko, Sov. Phys. Usp. 23 (1980) 21
    • (1980) J. Phys. C , vol.13 , pp. 2913
    • Mikeska, H.J.1
  • 16
    • 0003427157 scopus 로고    scopus 로고
    • edited by A. T. Skjeltorp and D. Sherrington, Kluwer Academic Publishers, Dordrecht
    • D. Loss, in Dynamical Properties of Unconventional Magnetic Systems edited by A. T. Skjeltorp and D. Sherrington, Kluwer Academic Publishers, Dordrecht 1998, p. 29
    • (1998) Dynamical Properties of Unconventional Magnetic Systems , pp. 29
    • Loss, D.1
  • 17
    • 0008502065 scopus 로고    scopus 로고
    • note
    • y, of spin waves transverse to the ladder
  • 25
    • 0008524079 scopus 로고    scopus 로고
    • note
    • A later analysis of the O(3) case in 1 + 1d by Nicopoulos and Tsvelik [24] begins by writing down the quadratic coupling form (Eq. 9) appropriate to the AF situation, but proceeds to apply the results of the exact solution to the model with linear coupling [22]. No explanation is provided that this procedure is justified
  • 29
    • 33646657428 scopus 로고
    • Before saturation there is no true long-range order, but the field imposes a quasi-long-range order of the XY-mode\ type: I. Affleck, Phys. Rev. B 43 (1991) 3215
    • (1991) Phys. Rev. B , vol.43 , pp. 3215
    • Affleck, I.1
  • 32
    • 0008442463 scopus 로고    scopus 로고
    • note
    • F is not renormalized according to Luttinger's theorem. Similarly, in a Luttinger liquid the Zeeman interaction is in general also renormalized [34]: in the RG treatment of this case, the Luttinger liquid parameters (Kσ) themselves become logarithmically dependent on the magnetic field alone [34] (cf. Eq. (35)). Neither of these results satisfies the scaling hypothesis of Ref. [29]
  • 33
    • 0008477876 scopus 로고    scopus 로고
    • note
    • We note that the gauge theory (Eq. (36)) is non-Abelian [29] an important consequence of which is that different field components need not renormalize in the same way. Thus the result of Eq. (35) does not conflict with the discussion of gauge invariance and RG methods introducing finite momentum cutoffs in Refs. [35, 36], which concerns the Abelian case


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