Convergence of eigenstate expectation values with system size

• URL: http://arxiv.org/abs/2009.05095v2
• Date: Thu, 24 Mar 2022 23:57:10 GMT
• Title: Convergence of eigenstate expectation values with system size
• Authors: Yichen Huang
• Abstract summary: 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 are lower bounded by $1/O(N)$.
• Score: 2.741266294612776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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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