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A proof of part of Haldane's conjecture on spin chains

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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.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, P.O. Box 708, 08544, Princeton, NJ, USA

    Ian Affleck & Elliott H. Lieb

  2. Department of Physics, Princeton University, P.O. Box 708, 08544, Princeton, NJ, USA

    Ian Affleck & Elliott H. Lieb

Authors
  1. Ian Affleck
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  2. Elliott H. Lieb
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Additional information

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. A proof of part of Haldane's conjecture on spin chains. Lett Math Phys 12, 57–69 (1986). https://doi.org/10.1007/BF00400304

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  • DOI: https://doi.org/10.1007/BF00400304

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