论文标题
具有系统尺寸的本征状期望值的收敛
Convergence of eigenstate expectation values with system size
论文作者
论文摘要
了解热力学极限中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，我们研究了本地操作员的本征态期望值的速度，因为系统尺寸差异，能量密度的平稳函数。在任何空间尺寸中的翻译不变量子晶格系统中，我们证明除了零尺寸的本地运算符外，有限尺寸的特征态期望值与上述平滑函数的偏差是由$ 1/o（n）$（$ n $ n $ n $ n of Systems systems systems Siges loce of上述平滑函数）。下边界均具有不管模型的可集成性或混沌性，并且在满足本征态热假说的系统中饱和。
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.
