Convergence of eigenstate expectation values with system size

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-09-10 DOI:10.4310/ATMP.2022.v26.n6.a5
Yichen Huang
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引用次数: 1

Abstract

Understanding the asymptotic behavior of physical quantities in the thermodynamic limit is a fundamental problem in statistical mechanics. In this paper, we study how fast the eigenstate expectation values of a local operator converge to a smooth function of energy density as the system size diverges. In translationally invariant systems in any spatial dimension, we prove that for all but a measure zero set of local operators, the deviations of finite-size eigenstate expectation values from the aforementioned smooth function are lower bounded by $1/O(N)$, where $N$ is the system size. The lower bound holds regardless of the integrability or chaoticity of the model, and is tight in systems satisfying the eigenstate thermalization hypothesis.
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特征态期望值随系统大小的收敛性
理解物理量在热力学极限下的渐近行为是统计力学中的一个基本问题。本文研究了局部算子的特征态期望值随系统大小的发散收敛到能量密度光滑函数的速度。在任意空间维度的平移不变系统中,我们证明了对于除测度零外的所有局部算子集,有限大小的特征态期望值与上述光滑函数的偏差下界为$1/O(N)$,其中$N$为系统大小。无论模型的可积性还是混沌性,下界都成立,并且在满足本征态热化假设的系统中是紧的。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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