Minimizing Couplings in Renormalization by Preserving Short-Range Mutual Information
- Working Paper
The connections between renormalization in statistical mechanics and information theory are intuitively evident, but a satisfactory theoretical treatment remains elusive. Recently, Koch-Janusz and Ringel proposed selecting a real-space renormalization map for classical lattice systems by minimizing the loss of long-range mutual information [Nat. Phys. 14, 578 (2018)]. The success of this technique has been related in part to the minimization of long-range couplings in the renormalized Hamiltonian [Lenggenhager et al., Phys. Rev. X 10, 011037 (2020)]. We show that to minimize these couplings the renormalization map should, somewhat counterintuitively, instead be chosen to minimize the loss of short-range mutual information between a block and its boundary. Moreover, the previous minimization is a relaxation of this approach, which indicates that the aims of preserving long-range physics and eliminating short-range couplings are related in a nontrivial way. Show more
Journal / seriesarXiv
Pages / Article No.
Organisational unit03781 - Renner, Renato / Renner, Renato
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