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Volumn 60, Issue 6, 1988, Pages 531-534

Extended Heisenberg models of antiferromagnetism: Analogies to the fractional quantum Hall effect

Author keywords

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Indexed keywords

EID: 0000678841 PISSN: 00319007 EISSN: None Source Type: Journal
DOI: 10.1103/PhysRevLett.60.531 Document Type: Article

Times cited : (276)

References (15)

4
- 0000021995
- (1985) Phys. Rev. B , vol.31 , pp. 5280
- Trugman, S.A.¹ Kivelson, S.²

5
- 84927870697
- R. P. Feynman, Statistical Mechanics, (Benjamin, New York, 1972);

6
- 35848960956
- and Phys. Rev. B 33 2481 (1986).
- (1985) Phys. Rev. Lett. , vol.54 , pp. 581
- Girvin, S.M.¹ MacDonald, A.H.² Platzman, P.M.³

7
- 84927870696
- The wave functions appear almost identical if the Laughlin state is written in a spherical geometry (Ref. 3): PSI = prodi < j ( uivj- viuj)m. The difference is that the Laughlin state is a product over all N ( N - 1 ) / 2 pairs of electrons, while the AKLT state is a product over the z N / 2 nearest-neighbor bonds.

10
- 0000800359
- (1980) Phys. Rev. B , vol.22 , pp. 4462
- Shenker, S.H.¹ Tobochnik, J.²

12
- 84927870693
- At k = 0, e.g., the lowest-lying excitation is a pair of elementary k = pi magnons. The numerical value of half the k=0 gap is Δ (0) / 2 apeq 0.36.

13
- 84927870692
- Let e1kvec and E2kvec be the lowest two eigenvalues with crystal momentum k vec. Then < k vec | ( H - E1kvec ) ( H - E2kvec ) | k vec > >= 0, from which Eq. (11) follows.

14
- 84927870691
- When S is half an odd integer, Eq. (13) yields a dimer state for all p (e.g., for S = p = case 1 over 2, | ψ > corresponds to an alternating chain of singlet pairs), and hence | ψ > is not a good trial ground state for lambda sufficiently close to zero.

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