TY - JOUR

T1 - Asymptotic behavior of macroscopic observables in generic spin systems

AU - Kuwahara, Tomotaka

PY - 2016/5/11

Y1 - 2016/5/11

N2 - 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.

AB - 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.

KW - fluctuations (theory)

KW - ladders and planes (theory)

KW - rigorous results in statistical mechanics

KW - spin chains

KW - structural correlations (theory)

UR - http://www.scopus.com/inward/record.url?scp=84969916998&partnerID=8YFLogxK

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U2 - 10.1088/1742-5468/2016/05/053103

DO - 10.1088/1742-5468/2016/05/053103

M3 - Article

AN - SCOPUS:84969916998

VL - 2016

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 5

M1 - 053103

ER -