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

Ian Affleck, Elliott Lieb

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321 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)57-69
Number of pages13
JournalLetters in Mathematical Physics
Issue number1
StatePublished - Jul 1 1986

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics


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