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16
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84926800772
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Gaplessness in the generic half-odd-integer antiferromagnetic chains was recently proven in Ref. 44.
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21
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84926800771
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Recently, a new class of extended (antiferromagnetic) Heisenberg models with exactly soluble ground states was introduced in Ref. 38. Excellent agreement with numerical results on the magnon spectrum in an extended S=1 chain has been obtained using a single-mode approximation (see Ref. 39).
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27
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84926822556
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This SU(N) model differs slightly from the fermionic one proposed by Affleck in Ref. 20. The difference lies in whether the total occupation of all species of bosons (or fermions) is on the order of 1, as in Ref. 20, or on the order of N, as in the present work and in Ref. 18.
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29
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84926822555
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In fact, the action is periodci under λi -> λi + 2 π i / beta. Integration along the entire imaginary axis therefore introduces an infinite constant factor multiplying the partition function. Later, when we examine the saddle-point approximation to Z, we will only consider the contribution from the saddle point along the real lambda axis and not its periodic images. This will precisely cancel the aforementioned infinite constant.
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30
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84926800769
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In the original Takahashi theory, Q is replaced by S in the expression for nk. At low temperature, Q - S = O ( T3/2 ), and the quoted low-temperature expansions are identical. The inclusion of Q rather than S constitutes an improvement of the original Takahashi theory, cf. Ref. 6, Sec. 27.
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31
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84926822554
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We thank B I. Halperin for pointing this out to us.
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37
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84926844465
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For reference, naive spin-wave theory (Ref. 40) gives a bandwidth 2/ pi times the exact des Cloiseaux-Pearson value.
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38
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0001457768
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An equivalent mean-field theory of the flux phase is discussed by
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(1988)
Phys. Rev. B
, vol.37
, pp. 3664
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Kotliar, G.1
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40
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0001672966
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(1987)
Phys. Rev. Lett.
, vol.59
, pp. 1613
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Shirane, G.1
Endoh, Y.2
Birgeneau, R.J.3
Kastner, M.A.4
Hidaka, Y.5
Oda, M.6
Suzuki, M.7
Muramaki, T.8
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42
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84926800768
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A. Auerbach and Daniel P. Arovas (unpublished).
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43
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84926800767
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We have not succeeded in going beyond the O ( S2 ) contribution to A (S) == limT->0 T ^ln xi for the square lattice antiferromagnet. The expected asymptotic form based on the sigma-model mapping is Aexp (S) = 2 π S (S+1).
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46
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84926822553
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Daniel P. Arovas and S. M. Girvin (unpublished).
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48
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84926800766
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Commun. Math. Phys. (to be published).
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