本征态期望值随系统尺寸的收敛性
Convergence of eigenstate expectation values with system size
AI总结：
本文研究了任意维度平移不变量子格点系统中局部算子本征态期望值随系统尺寸的收敛速度，证明其偏差下界为 $1/O(N)$，该下界与模型可积性或混沌性无关，并在满足本征态热化假说的系统中达到饱和。
摘要：
理解热力学极限下物理量的渐近行为是统计力学中的一个基本问题。在本文中，我们研究了当系统尺寸发散时，局部算子的本征态期望值以多快的速度收敛为能量密度的光滑函数。在任意空间维度的平移不变量子格点系统中，我们证明对于除零测集外的所有局部算子，有限尺寸本征态期望值偏离上述光滑函数的偏差下界为 $1/O(N)$，其中 $N$ 为系统尺寸。该下界与模型的可积性或混沌性无关，并在满足本征态热化假说的系统中达到饱和。
英文摘要：
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 translation-invariant quantum lattice 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 saturated in systems satisfying the eigenstate thermalization hypothesis.
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