A Berry-Esseen theorem is proven for local observables in quantum lattice systems with finite correlation length, yielding convergence to normality with error O(N^{-1/2} polylog N).
First, one can give the trivial bound: c3 e−(1−c1) ω2 4 Z ω 0 dω1 e(1−c1) ω2 1 4 ≤c 3 Z ω 0 dω1 =c 3 ω ,(49) where we used Hölder’s inequality
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A Berry-Esseen Bound for Quantum Lattice Systems
A Berry-Esseen theorem is proven for local observables in quantum lattice systems with finite correlation length, yielding convergence to normality with error O(N^{-1/2} polylog N).