### 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.

Original language | English (US) |
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Pages (from-to) | 57-69 |

Number of pages | 13 |

Journal | Letters in Mathematical Physics |

Volume | 12 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 1986 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

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## Cite this

Affleck, I., & Lieb, E. (1986). A proof of part of Haldane's conjecture on spin chains.

*Letters in Mathematical Physics*,*12*(1), 57-69. https://doi.org/10.1007/BF00400304