A Proof of Part of Haldane's Conjecture on Spin Chains
May 5, 1986
18 pages
Published in:
- Lett.Math.Phys. 12 (1986) 57
DOI:
Report number:
- Print-86-0362 (PRINCETON)
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Abstract: (Springer)
It has been argued that the spectra of infinite length, translation and U(1) invariant, anisotropic, antiferromagnetic spin s chains differ according to whether s is integral or 1/2 integral: There is a range of parameters for which there is a unique ground state with a gap above it in the integral case, but no such range exists for the 1/2 integral case. We prove the above statement for 1/2 integral spin. We also prove that for all s, finite length chains have a unique ground state for a wide range of parameters. The argument was extended to SU(n) chains, and we prove analogous results in that case as well.References(12)
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