Universal Renyi mutual information in classical systems: the case of kagome ice

TL;DR

This paper investigates the Renyi mutual information in classical kagome ice systems, establishing a universal subleading term for chiral kagome ice and analyzing its robustness against defects.

Contribution

It connects classical mutual information with quantum entanglement, predicts a universal term in chiral kagome ice, and verifies this through numerical computations.

Findings

Universal subleading term in chiral kagome ice mutual information

Chiral kagome ice mapped to Lifshitz critical field theory

Nonchiral kagome ice is topologically trivial

Abstract

We study the Renyi mutual information of classical systems characterized by a transfer matrix. We first establish a general relationship between the Renyi mutual information of such classical mixtures of configuration states, and the Renyi entropy of a corresponding Rokhsar-Kivelson--type quantum superposition. We then focus on chiral and nonchiral kagome-ice systems, classical spin liquids on the kagome lattice, which respectively have critical and short-range correlations. Through a mapping of the chiral kagome ice to the quantum Liftshitz critical field theory, we predict a universal subleading term in the Renyi mutual information of this classical spin liquid, which can be realized in the pyrochlore spin ice in a magnetic field. We verify our prediction with direct numerical transfer-matrix computations, and further demonstrate that the nonchiral kagome ice (and the corresponding quantum Rokhsar-Kivelson superposition) is a topologically trivial phase. Finally, we argue that the universal term in the mutual information of the chiral kagome ice is fragile against the presence of defects.