### Abstract

This work clarifies a fundamental relationship between spectral gap and ground state properties, where the spectral gap means the energy difference between the ground state and the first excited state. In short-range interacting systems, the well-known exponential clustering theorem has been derived for the ground states: the bipartite correlations decay exponentially beyond a finite localization length, which is smaller than the inverse of the spectral gap. However, in more general systems including long-range interacting systems, the problem of how to characterize universal ground state structures by reference to the spectral gap is an ongoing challenge. Recently, for such systems, another fundamental constraint dubbed local reversibility has been proved for arbitrarily gapped ground states; as a consequence, it also results in the exponential concentration of the probability distribution of macroscopic observables. In this paper, we extend this kind of asymptotic behavior to more general setups.

Original language | English |
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Article number | 053103 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2016 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2016 May 11 |

### Keywords

- fluctuations (theory)
- ladders and planes (theory)
- rigorous results in statistical mechanics
- spin chains
- structural correlations (theory)

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2016*(5), [053103]. https://doi.org/10.1088/1742-5468/2016/05/053103