We report on a rigorous operator-algebraic renormalization group scheme and construct the free field with a continuous action of translations as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets. Causality follows from Lieb-Robinson bounds for harmonic lattice systems. The scheme is related with the multiscale entanglement renormalization ansatz and augments the semicontinuum limit of quantum systems.

中文翻译：

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算子代数重整化和小波

我们报告了严格的算子代数重整化群方案，并使用小波理论构造具有连续平移作用的自由场作为哈密顿点阵系统的标度极限。重整化群步长由标度方程确定，该方程用紧密支持的小波涂抹的连续场识别格子可观测量。因果关系遵循谐波晶格系统的 Lieb-Robinson 界限。该方案与多尺度纠缠重整化 ansatz 相关，并增加了量子系统的半连续极限。