Recently, a novel real-space renormalisation group (RG) algorithm was introduced. By maximising an information-theoretic quantity, the real-space mutual information, the algorithm identifies the relevant low-energy degrees of freedom. Motivated by this, we investigate the information theoretic properties of coarse-graining procedures, for both translationally invariant and disordered systems. We prove that a perfect RSMI coarse-graining does not increase the range of interactions in the renormalized Hamiltonian, and, for disordered systems, suppresses generation of correlations in the renormalized disorder distribution, being in this sense . We empirically verify decay of those measures of complexity, as a function of information retained by the RG, on the examples of arbitrary coarse-grainings of the clean and random Ising chain. The results establish a direct and quantifiable connection between properties of RG viewed as a compression scheme, and those of physical objects i.e.~Hamiltonians and disorder distributions. We also study the effect of constraints on the number and type of coarse-grained degrees of freedom on a generic RG procedure.

中文翻译：

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基于信息论的最优重归一化组变换

最近，引入了一种新颖的实空间重归一化组（RG）算法。通过最大化信息理论量（真实空间互信息），该算法可以识别相关的低能量自由度。因此，我们研究了平移不变和无序系统的粗粒度过程的信息理论特性。我们证明了完美的RSMI粗粒度不会增加重归一化的Hamilton系统中的相互作用范围，并且对于这种情况，对于无序系统而言，抑制了重归一化的无序分布中相关性的产生。我们根据干净随机的伊辛链的任意粗粒度示例，根据RG保留的信息，以经验方式验证那些复杂性度量的衰减。结果在被视为压缩方案的RG特性与物理对象（即〜哈密顿量和无序分布）的特性之间建立了直接且可量化的联系。我们还研究了通用RG程序上约束对粗粒度自由度的数量和类型的影响。