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).
For allN >max{e 2,4ξ (logN) 2 log 2 }we have: ∆≤f 1(N) (logN) 2D √ N ,(17) for some explicit functionf1(N)(see Eq.(31)) which can be upper-bounded by a constant
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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).