## Abstract

Lieb, Schultz and Mattis (LSM) (1961 Ann. Phys., NY 16 407) studied the S = 1/2 XXZ spin chain. The theorems of LSM's paper can be applied to broader models. In the original LSM theorem the nonfrustrating system was assumed. However, reconsidering the LSM theorem, we can extend the LSM theorem for frustrating systems. Next, several researchers tried to extend the LSM theorem for excited states. In the cases , the lowest energy eigenvalues are continuous for wave number q. But we found that their proofs were insufficient, and improve upon them. In addition, we can prove the LSM theory without the assumption of the discrete symmetry, which means that LSM-type theorems are applicable for Dzyaloshinskii-Moriya type interactions or other nonsymmetric models.

Original language | English |
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Article number | 375001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 37 |

DOIs | |

Publication status | Published - Sept 18 2015 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy