### Abstract

For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, with arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C log L)/L. This result can be regarded as a multi-dimensional Lieb-Schultz-Mattis theorem [14] and provides a rigorous proof of the main result in [8].

Original language | English (US) |
---|---|

Pages (from-to) | 437-472 |

Number of pages | 36 |

Journal | Communications in Mathematical Physics |

Volume | 276 |

Issue number | 2 |

DOIs | |

State | Published - Dec 2007 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'A multi-dimensional Lieb-Schultz-Mattis theorem'. Together they form a unique fingerprint.

## Cite this

Nachtergaele, B., & Sims, R. (2007). A multi-dimensional Lieb-Schultz-Mattis theorem.

*Communications in Mathematical Physics*,*276*(2), 437-472. https://doi.org/10.1007/s00220-007-0342-z