Abstract
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.
Work partially supported by U.S. National Science Foundation grant PHY80-19754 and by the A.P. Sloan Foundation.
Work partially supported by U.S. National Science Foundation grant PHY-85–15288.
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Affleck, I., Lieb, E.H. (1986). A Proof of Part of Haldane’s Conjecture on Spin Chains. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Condensed Matter Physics and Exactly Soluble Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06390-3_17
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DOI: https://doi.org/10.1007/978-3-662-06390-3_17
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