Geometric mutual information at classical critical points

Abstract

A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$ is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2d conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to $c$. This makes it possible to extract $c$ in classical simulations, which we demonstrate for the critical Ising and 3-state Potts models.

arXiv comment5 pages. v3: published version

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• Mutual Information, Neural Networks and the Renormalization Group
• Shannon and Rényi mutual information in quantum critical spin chains
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Post measurement bipartite entanglement entropy in conformal field theories
• Generalized mutual informations of quantum critical chains
• Entanglement and classical fluctuations at finite-temperature critical points
• Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains
• A generalization of the maximum entropy principle for curved statistical manifolds
• Anomalous metastability in a temperature-driven transition
• Entanglement entropy, dualities, and deconfinement in gauge theories
• The classical mutual information in mean-field spin glass models
• Shared information in classical mean-field models
• Thermodynamics of exponential Kolmogorov-Nagumo averages
• Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model
• Critical scaling of the mutual information in two-dimensional disordered Ising models
• A Rényi entropy perspective on topological order in classical toric code models
• Entropy Governed by the Absorbing State of Directed Percolation
• Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model
• Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model
• Geometric Structures Induced by Deformations of the Legendre Transform
• Relative Entropy and Mutual Information in Gaussian Statistical Field Theory
• Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics