### Abstract

We consider the kink (infinite volume nontranslationally invariant ground states) of the ferromagnetic XXZ models on the multi-dimensional lattices. We obtained the following results: (i) The pure states satisfying the local zero energy condition are necessarily product states, (ii) The Hamiltonian in the GNS representation of the kink has no gap between the ground-state eigenvalue and the rest of the spectra.

Original language | English |
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Pages (from-to) | 229-239 |

Number of pages | 11 |

Journal | Letters in Mathematical Physics |

Volume | 42 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1997 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics