Asymptotic behavior of macroscopic observables in generic spin systems

Tomotaka Kuwahara

研究成果: Article査読

11 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号053103
ジャーナルJournal of Statistical Mechanics: Theory and Experiment
2016
5
DOI
出版ステータスPublished - 2016 5月 11

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • 統計学、確率および不確実性

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