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.

5 pages. v3: published version

References in corpus (6)

• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Universal behavior beyond multifractality in quantum many-body systems
• Rényi entropy of a line in two-dimensional Ising models
• Finite Temperature Critical Behavior of Mutual Information
• Finite size behaviors of critical Ising model on a rectangle with free boundaries
• Rectangular amplitudes, conformal blocks, and applications to loop models

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• A generalization of the maximum entropy principle for curved statistical manifolds
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• Entanglement entropy, dualities, and deconfinement in gauge theories
• The classical mutual information in mean-field spin glass models
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• 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
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• 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