### 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 |
---|---|

Article number | 375001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 37 |

DOIs | |

Publication status | Published - Sep 18 2015 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*48*(37), [375001]. https://doi.org/10.1088/1751-8113/48/37/375001

**Extension of the Lieb-Schultz-Mattis theorem.** / Nomura, Kiyohide; Morishige, Junpei; Isoyama, Takaichi.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 48, no. 37, 375001. https://doi.org/10.1088/1751-8113/48/37/375001

}

TY - JOUR

T1 - Extension of the Lieb-Schultz-Mattis theorem

AU - Nomura, Kiyohide

AU - Morishige, Junpei

AU - Isoyama, Takaichi

PY - 2015/9/18

Y1 - 2015/9/18

N2 - 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.

AB - 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.

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U2 - 10.1088/1751-8113/48/37/375001

DO - 10.1088/1751-8113/48/37/375001

M3 - Article

AN - SCOPUS:84940056763

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 37

M1 - 375001

ER -